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H!) ll>NOIS,^n no,not> inois,IByqL}?yqBy` hfȱyq y`20:11:"IS POSITIVE."C(A.2:BD.2:C1:HC7:L114:L213:9000i222:24:255:"Y= 2X@U/ + 2X + 1"s<4000>24:23:"@@RETURN@@ TO CONTINUE":0:174,177189,177:22:24:"Y= 2X@U/ + 2X + 1":HC0:9000?10:1:E21,13A **PLACE SWITCH HE255:"@P":#####80310:2:"L@@OOKING AT THIS"I:"EQUATION...."i14:4:"Y= 2X@U/ + 2X + 1"pP16:2:"...WE SEE THAT ITS":"GRAPH OPENS @@UPWARD@@" :"SINCE A "5:47,14957,14957,16347,16347,149: BOX THE AD.5:C1:HC7:9000~4000C24:23:"@@RETURN @@TO CONTINUE"22:24:"Y=-3X@U/ + 4X + 5": ERASE IT FOR NEW SCREEN0:174,177189,177: ERASE UNDERLINE HC0:900010:1:255:E21,13:ERASE BLOCKLO%(24580)256(24589):820:2:"OR @@DOWNWARD @@IF A IS"?B22:2:"@@NEGATIVE.@@"sL255:22:24:"Y= 3X@U/ + 4X + 5":255: ####75V22:24:"Y=-3X@U/ + 4X + 5": PRINT IT`7:174,177185,177: UNDERLINE 3jHC0:9000: ERASE PARABOLAtL112:L214:A.25:B0)7:179,177185,177: UNDERLINE 3O20:2:"(NOTICE THE POSITIVE 3) eZS.75:D: DELAYL114:L212:A.25:BD.5:C1:HC7:9000$P)255.20:2:"(NOTICE THE POSITIVE 3)": FOR ERASE00:174,177189,1773255: ####75#THIS:"HC0:9000CL112:L214:A.25:HC7::BD.5:C1:9000JPr16:2:"@@T@@HE GRAPH OPENS @@UP-":"WARD @@IF A IS @@POSITIVE,"HC0:9000: ERASE LAST GRAPH255: #####7522:24:"@@Y= 3X@U/ + 4X + 5" 255: ####15 DRAW AXES -"@P": PROP. SPACINGK10:32:"Y":16:23:"X"cSD0: RESET B TESTx255: ###### 7510:2:"@@I@@TS SHAPE IS SIMILAR TO"12:17:"THIS:"L114:L212:A.25:BD.5:HC7:C1:9000P14:14:"@@O@@R 0@  @@@@@@@@@@  @0@p~@?@80p `xp``@H@8```p@ @0  @ 0@ @@@@ @@@ @@@0 ``p@0p~?@8@ @ 0@A>@ @ @0 >A @ @@@ @ 8@` 0@` @0 ` 0@  @@ @@  p`xp`@`  @@@            0  0 CH       >     !!!!!     ,> "8  @     ?? ||ByqL}?yqBy` hfȱyq y`TB|`{} _\@[]  ~ ^CH  PHED ON THE SCREEN."G-*"@0":16:9:"Y = @@A@@X@U/ + @@B@@X + @@C@@"}-418:2:"@@V@@ALUE OF @@A@@";:A$:T$A$:T1:5500-5A%T%-6T6ĺ"@$":18:13:" ":T0:2100-7A%5A%5A%0ĺ"@$":18:13:" ":T0:2100!.>20:2:"@@V@@M@@AKE UP AN EQUATION BELOW,"::"SUBSTITUTING A NUMBER BETWEEN 5 AND -5",5:2:"FOR @@A,@@ AND NUMBERS BETWEEN 20 AND -20",7:2:"FOR @@B@@ AND @@C@@.",255:10:1:"@@T@@YPE THEM IN, PRESS @@RETURN@@, AND YOU'LL SEE"- 12:9:"IT GRAIS NEG-"+18:2:"ATIVE,"*+ZS.5:DR+7:112,42126,42: UNDERLINE -4 +18:8:"IT OPENS IN THE NEGATIVE (DOWN)":20:2:"DIRECTION."+5:1,170279,170+5000+N:255:"@P": BACK TO 150 LATER####L,1:2:"N@@OW YOU TRY IT. 5:1,56279,56: ORANGE LINE*255:10:2:"@@I@@N WHICH DIRECTION, UP OR DOWN, WILL THE"::"PARABOLA OPEN? @@";:I: ####100 *A"@LDOWN":ZA%1970*16:2:"W@@RONG.":1975*16:2:"R@@IGHT."+"@P":16:9:"@@S@@INCE THE LEADING TERM 22:1:"@@T@@HE RESULTING EQUATION"::"IS THE AXIS OF SYMMETRY."^)v4000: ABBREV. RETURN)N:B8:255:"@P": BACK TO 150 LATER####### )1:2:"D@@ESCRIBE HOW THE GRAPH OF THIS EQUATION"::"WOULD LOOK:")5:13:"Y = -4X@U/ + 5X + 9"*"IN DRAWING THE GRAPH."A(:14:1:"@@T@@O FIND IT, SUBSTITUTE"`(D16:4:"INTO THE FORMULA"(N19:7:"X = - ":X85:Y138:"B":7:80,14894,148:X80:Y152:"2A"(X5:37,131101,131101,16337,16337,131: BOX THE FORMULA(b19:16:"."C)lA' ZS.2:D:'1:211,72211,160: DRAW AXIS OF SYMM.U'ZS.1:D:255:####200'22:24:"AXIS OF SYMMETRY":7:162,165168,154207,140: DRAW ARROW '!198,140206,140201,146: ARROWHEAD'&P(010:1:"@@S@@UCH A LINE IS HELPFUL"::DING IT INTO TWO HALF-PARABOLAS,"G&:"MIRROR IMAGES OF EACH OTHER."p&7:1,50279,50: DRAW DIVIDING LINEw&P&5:151,68277,68277,182151,182151,68: DRAW GRAPH BOX 'L118:L217:A.2:BD.2:C10:HC7:9000: DRAW SIMPLE PARABOLC , A LINEAR"::"EQUATION. @@S@@INCE A PARABOLA IS A CURVE,"~%:"THIS EQUATION CAN'T FORM A PARABOLA"::"WHEN A = 0 ."%5000%N:B7:LO%(24588)256(24589):255:"@P"%1:1:"E@@VERY PARABOLA HAS AN @@AXIS OF SYMMETRY@@,"!&:"DIVI"0";:FY:16:"0";:FY8$7:16:"0": RESTORE LAST 0F$ZS.25:Dw$7:105,42126,60:126,42105,60: CROSS OUT$ZS.19:D$ZS.1:D:0:H4064:98,H140,H:H: ERASE CROSSOUT $255:"@P": ###150>%11:2:"@@T@@HIS LEAVES Y = BX + #^4:15:"WILL DROP OUT."9#h"@0": STANDARD SPACINGu#r7:11:"Y = AX@U/ + BX + C": DRAW INITIAL EQUATION }#w50#{9:6:"0":ZS1:D#|FX615:9:FX:"0";:"0";:FX#9:16:"0":7:16:"A": ERASE LETTERS $FY971:FY:16:"5000>""N:B6:255: #####BACK TO 255 LATERO",2:3:"@@A"~"65:9,523,523,199,199,5: BOX THE A "@2:6:"CANNOT BE EQUAL TO ZERO, BECAUSE IF""J4:3:"IT IS, X@U/""T5:65,1885,1885,3565,3565,18: BOX THE X2 ION OF THE SIGN OF"::" A "P!5:3,11817,11817,1303,1303,118: BOX THE At!16:4:". @@T@@HE POSITIVE Y"!127,118141,118141,130127,130127,118: BOX THE Y !18:1:"DIRECTION IS UP, AND"::"THE NEGATIVE DIREC-"::"TION IS DOWN."N@@ TO CONTINUE":0:174,177197,177:22:23:"Y = -2X@U/ + 2X + 1"` HC0:9000: ERASE GRAPH 10:1:E21,13: ERASE TEXT BLOCK  END ERASING SEQUENCE 255: ######BACK TO 90!10:1:"T@@HE PARABOLA ALWAYS"::"OPENS IN THE DIREC-"::"T10:"IS@@ NEGATIVE@@.">7:41,9852,98: UNDERLINE -2 jL114:L215:A.2:BD.2:C1:HC7:900022:23:255:"Y = -2X@U/ + 2X + 1"7:181,177194,177: UNDERLINE AT BOTTOM 4000 START ERASING SEQUENCEC 24:23:"@@RETURRE#C255: #####BACK TO 80 LATEREF10:2:"T@@HIS EQUATION...."gP12:3:"Y = -2X@U/ + 2X + 1"Z14:2:"WILL FORM A @@DOWNWARD@@"::"OPENING PARABOLA,"d:"SINCE A "n5:45,13557,13557,14545,14545,135: DRAW BOX FOR Ax18:48:9:"@@C@@IRCLES DESCRIBED BY THIS"t>10:2:"FORM OF EQUATION ALWAYS HAVE THEIR"::"CENTER AT THE ORIGIN."~H5000RN: THIRD QUESTION #####\1:2:"W@@HAT IS THE RADIUS OF THIS CIRCLE?"f3:12:"4X@U/ + 4Y@U/ = 40"'p5:2:"@@P@65,90151,90151,785000AN: NEW SCREEN#####!!!!"#"S$!%v 2:2:"W@@HERE IS THE CIRCLE'S CENTER LOCATED?" 4:12:"3X@U/ + 3Y@U/ = 27"6:16:ZL%10:IA"@LORIGIN":O"0,0" ZA%1Ģ8:2:"R@@IGHT.":820*8:2:"W@@RONG."(29:IA"3"4ZA%1Ģ7:2:"@0R@@IGHT.":720L7:2:"@0W@@RONG."7:9:"@P@@D@@IVIDING THROUGH BY 3, 27 BECOMES"9:2:"9 , WHOSE SQUARE ROOT IS 3 . @@S@@O THE"11:2:"CIRCLE HAS A RADIUS OF 3 ."5:151,78165,781XB%0A%022610!:OXB%022630,:PX22630>:RXS$"-":22700I:fXS$" ":X15:4:S$:X36:Y107:BTEM:7:31,11545,115:X36:Y118:AEM::tYP1210(A37):3:P1,5P1,170:: AXIS OF SYMM.D SYMM.P(B%):AEM(A%)%9JXB%0A%022610:9MXB%0A%022610J9OXB%022630U9PX22630g9RXS$"-":22700r9fXS$" "9X15:4:S$:X36:Y107:BTEM:7:31,11545,115:X36:Y118:AEM:9tYP1210(A37):3:P1,5P1,170:: AXIS OF SYMM.A%022610:MY8K#XY2122X8P#HC:XY,Y&8Z#X,8d#38*7C8+X99.078 +Y%((XXA%)XB%C%):PY%88Y%:PX%1477X63:PY%1PY%175ĂX8+PY%1PY%175ı8+PX%,PY%8 +X8*+821:1:(15);"F":8 N SUBROUTINE FOR AXES9HX15:1:"X =":BTEM,L:24583,H7q77XP1:X1682722:PX(P)X:PP1:X]7bP1:Y168801:PY(P)Y:PP1:Yc7li7@p74!7{79!R127>!V:XX:" XYYYYYZ":V1:XX:"12 34":V2:XX:"5666667":R7H!07R!7(#72#XL1L2.57<#Y(XXA)BDXC8F#Y12416368,0:5050,6(16384)141Ĺ16368,0:665020j6SD1:B5060,100,350,450,580,850,1570,1750,1920p66|(T$)0T6:6}T1$(T$,1)6~(T1$)54(T1$)42T%((T$,3)):"@%":6T6: 7pH((LO%2156)256):L(LO%2156)256H:24582"@$":4500O5"@%":A$"N"Ģ23:21:E20,2:"@@":4000:2350: END******r5N:"@@":255:2090:######200516368,0:255:24:G0Ė9:"@@P@@RESS@@ RETURN @@TO CONTINUE":50205G0:2:"@@P@@RESS@@ RETURN @@TO CONTINUE" 6(16384)194ĹOF THE X AXIS."4t 4500#4~ 2350.4 255:94255:q4255:24:23:"@@RETURN @@TO CONTINUE":16368,0:P4ZK%66400344B100,100,350,450,580,850,1570,1750,1920,19904 522:1:"@@T@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"22900: DRAW AXIS OF SYMM.43ZS1.75:D: DELAY>345003. N:12:10:"@HO@LNE MOMENT PLEASE...":(13);(4)"PR#0":(13);(4)"RUN SECOND PART (2)"3` 15:10:". @@I@@T CAN'T"4j 17:1:"BE SHOWN HERE, SINCE"::"IT LIES BEYOND THE"::"RANGE 9:5:"POSITIVE.":2240/29:5:"NEGATIVE."D2A22A%:A3B%A2211:1:"@@T@@HE EQUATION OF THE"::"AXIS OF SYMMETRY IS"222600: FIND EQUATION FOR -B/2A2A39A392400215:8:",SHOWN BY THE"217:1:"LINE DOWN THE MIDDLE:"3###2001r11000: DRAW GRAPH01u255:####150g1z1:12:"@@N@@OTICE":3:1:"THAT THE GRAPH OPENS"1A%0Ģ5:1:"@@UPWARDS@@":220015:1:"@@DOWNWARD@@"15:9:",SINCE THE"17:1:"VALUE YOU CHOSE FOR"19:1:"@@A@@ IS"2A%0įX141:Y93:"": CTRL-V,CTRL-Q (-9)v0jX262:Y93:"":X192:Y5:"":X213:Y168:"": 9,+87,-870k"@P":255:###1500p1:1:"@@H@@ERE IT IS."1q255:X175:Y181:"Y=";A%;"X@U/+";B%;"X+";C%: WRITE EQUATION AT BOTTOM ####20?/KC%20C%20C%0ĺ"@$":22:13:" ":T0:2120Z/RN:: GRAPHING SCREEN/\5:137,1277,1277,175137,175137,1: DRAW BOX /f6:147,88273,88:210,5210,172:2:32:"@@Y":X141:Y85:"X": DRAW AXES/h"@P": PROP.SPAC.)0i@@ALUE OF @@B@@";:B$:T$B$:5500+.?B%T%Y.@T6ĺ"@$":20:13:" ":T0:2110.AB%20B%20B%0ĺ"@$":20:13::" ":T0:2110.H22:2:"@@V@@ALUE OF @@C@@";:C$:T$C$:5500.IC%T%/JT6ĺ"@$":22:13:" ":T0:21('&%$#":Y60:X90:"= !":Y68:X90:"- 9":Y76:X90:"012345678@S")5:90,68151,68:X160:Y60:"MAJOR")P)12:2:"AND THE MINOR DIAMETER IS THE WIDTH:"*X90:14:"@F:*)('&%$#":15:X90:"= !":16:X90:"- E@@LLIPSE":5:128,132146,1327(5000: PRESS RETURNa(N:255:B8:"@P": SETTINGS ########(2:2:"E@@VERY ELLIPSE HAS A MAJOR DIAMETER AND A"::"MINOR DIAMETER. @@T@@HE MAJOR DIAMETER IS THE"::"LENGTH OF THE ELLIPSE,"T)X90:Y52:"@F:*)" FG HI":13:20:" JK LM":14:20:" @@U @@UC"m'15:20:" WXY @@B":16:20:" DEFGHVW"'17:20:" @@N@@X@@PQRST":18:20:" VWXY Z@@AY":19:20:"C@@G @@DEFGHVJ":20:20:"KL MN":21:20:" OPQRRRST@@G"(17:12:"@S@@RED ON THE ORIGIN. @@I@@T'S"f&8:3:"FORMED BY A CONE CUT AT AN ANGLE NOT"::"TOUCHING ITS BASE:"&LO%(24588)256(24589)&H((LO%11281028)256):L(LO%11281028)256H:24582,L:24583,H:'10:20:"@F ABC":11:20:" D E":12:20:115159,115159,135156,131: SQUARE ROOT B%n16:27:"."L%s5000u%xN:255:B7:"@P": SETTINGS######&2:3:"I@@F @@A, B, @@AND @@C@@ HAVE THE SAME SIGNS BUT"::"@@A ";(24);" B,@@ THE EQUATION WILL DESCRIBE AN"::"@@ELLIPSE,@@ CENTE213,76127,76127,60($F PAUSE ######$P12:2:"@P@@GRAPHS AS A @@CIRCLE@@ WITH CENTER AT THE"::"ORIGIN, WHOSE RADIUS CAN BE PREDICTED"$Z16:2:"BY FINDING THE VALUE OF":X165:Y117:"@@C":X165:Y128:"A@@":7:161,126173,1261%d7:175,ON"h#(6:13:"@0@@A@@X@U/ + @@B@@Y@U/ = @@C@@":5:77,34179,34179,5477,5477,34: EQUATION & BOX #- PUT PAUSE HERE#########29:2:"WHEN @@A = B@@":43,6087,6087,7643,7643,60: BOX & A=B $<9:15:"AND @@A, B, C > 0":127,60213,60CH IS THE SQUARE"::"ROOT OF":X60:Y91:"@@C":X60:Y100:"A@@":7:56,9970,99"13:12:"IN YOUR":15:1:"EQUATION.""4500: TRY ANOTHER?"A$"Y"1050"N:255:B6:"@P": SETTINGS #2:2:"T@@HUS WE HAVE LEARNED THAT ANY EQUATI000%!RAD(C%A%):RAD$((RAD),4)Q!RAD1RAD$((RAD),4)" UNITS,":1238o!RAD$((RAD),4)" UNIT,"!1:1:"@@T@@HIS IS A ROUGH"::"GRAPH OF YOUR EQUA-"::"TION. @@N@@OTICE THAT"::"THE CIRCLE HAS A"::"RADIUS OF ";RAD$U"11:1:"WHI ** BEGIN COMMENTS ABOUT GRAPH> (C%)(.5((A%)))1235 1:1:"@@T@@HE VALUE YOU CHOSE"::"FOR @@C@@ IS TOO SMALL TO"::"FORM A CIRCLE BIG EN-"::"OUGH TO SHOW HERE."!10:1:"@@P@@RESS @@RETURN@@ TO TRY":12:7:"AGAIN.":16368,0:P:1)0(T$)641170t1200F"@$":14:31:(T$)1):T0:R:1105y18:2:"P@@RESS @@RETURN@@ TO SEE THE GRAPH."16368,0:P:ZK%131205N: NEW SCREEN FOR GRAPHING THE EQUATION12000: DRAW AXES & BOX9500K.2:11000! "@$":11:17:(ZA$)1):T0:R:1090KI(A%)1L$" NEGATIVE ":1100_JL$" POSITIVE "L14:2:"T@@YPE A";L$;"VALUE FOR @@C@@ "Q14:30:R:I:T$ZA$:5500VC%T%`T61170j(A%)11138oT%64T%01170p1200r(T$4:13:"@0A@@X@U/ + @@B@@Y@U/ = @@C@@"\.7:2:"@@T@@YPE A VALUE BETWEEN 5 AND -5 FOR"89:2:"@@A@@ AND @@B@@ (@@A = B@@ IN A CIRCULAR EQUATION)"B11:16:I:T$ZA$:5500CA%T%:B%T%DT61095EA%5A%5A%01095F1097&GYOU WOULD LIKE TO SEE SOME OF YOUR"::"OWN CIRCULAR EQUATIONS GRAPHED, PRESS"::"@@RETURN. O@@THERWISE PRESS @@ESC@@ TO CONTINUE."16368,0:P:ZK%27ZK%13ZK%661030ZK%271300ZK%66650N:255:"@P": SETTINGS ########'$@ BECOME 10."::"@@T@@HE SQUARE ROOT OF @@C@@ IS THE RADIUS,"b18:2:"WHICH IN THIS CASE IS"7:182,133164,133164,144162,141: SQR.RT.18:25:"10 ."5000: PRESS RETURNN:B255:B5:"@P": SETTINGS #######2:2:"I@@F @RESS THE & KEY IF YOU NEED A SQUARE"Bz7:13:"ROOT SYMBOL."Q10:17:IeA""ZA%1Ģ12:2:"R@@IGHT!":94012:2:"W@@RONG.">12:9:"@@F@@IRST DIVIDE THROUGH BY 4 (THE":14:2:"VALUE OF @@A@@ AND @@B@@), MAKING @@C@(15);"F":*96HCH7:HC2(HC2)14020H96X1H710:X2H74:14030_96X1H711:X2H7396Y1V811:Y2V83:5:X1,Y1X2,Y1X2,Y2X1,Y2X1,Y1:9hBLO%(24588)256(24589):H((LO%2156)256):L(LO%2156)256H:24582,L:24583,H: : N SUBROU.6:147,88273,88:210,5210,167:2:32:"@@Y":X141:Y85:"X": DRAW AXES e8."@P": PROP.SPC.8/ZY8827:208,ZY213,ZY:ZY:ZY881677:208,ZY213,ZY:ZY8/7:ZX2102778:ZX,86ZX,89:ZX:ZX2101478:ZX,86ZX,89:ZX8/ 921:1:7 +PY1PY17511028:7+PYPYH%:P9P9H%:PX,PY:PX,P9A7+X[7+J11030,11031:11035}7+IL3:LL4:SK:XILS:110107+IL4:LL2:S.08:110107+H%0:7. SUBROUTINE FOR AXIS & BOX7.5:137,1277,1277,177137,177137,1: ORANGE BOX O822:25:A%;"X@U/ + ";B%;"Y@U/ = ";C%:26*J0:7o6*P10:L1(((C%A%)))1::L2(L1):L3.666L1:L4.666L26*S.08:IL1:LL36+JJ1:XILS6+Y1(C%(A%(X2)))B%6+O886 +Y10110286 +Y(Y1):PY88(Y7):P988(Y7):PX1478X63:H0l 5@54!759!R12^5>!V:XX:" XYYYYYZ":V1:XX:"12 34":V2:XX:"5666667":Re5H!0k5R!q5(#52#XL1L2.55<#Y(XXA)BDXC5F#YY455K#XYX235P#HC:PX(XY),PY(Y)5Z#X5d#5% ** SUBROUTINE FOR EQUATION AT BOTTOM'6&%UN PART ONE (1)"$4|(T$)0T6:44}T1$(T$,1)c4~(T1$)58(T1$)42T%((T$,3)):"@%":n4T6:4pH((LO%2156)256):L(LO%2156)256H:24582,L:24583,H4q4XP1:X1682721:PX(P)X:PP1:X4bP1:Y168802:PY(P)Y:PP1:Y524:9:"@@P@@RESS@@ RETURN @@TO CONTINUE":5020S3(16384)194Ĺ16368,0:5050r3(16384)141Ĺ16368,0:|350203B5070,100,200,300,650,1000,1300,1400,1500,1600,170034N:12:10:"@HO@LNE MOMENT PLEASE...":36860,170:(13);(4)"RX1497X63#2JPY80PY175418552TPX,PY:PX,P9<2YXB2f222:1:"@@T@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"ĺ"@$":45002"@%":A$"N"įX147:Y178:E20,1:24:21:"RETURN@@ TO CONTINUE":P:2N:"@@":255:0316368,0:255:NTINUE":P1ZK%664003!1F1B100,100,200,300,650,1000,1300L1u17: FOR CIRCLE GRAPHS 1L1(((C%A%)))1:L201"XL1L2.21,Y1(C(A(X2)))B1-Y1041801.Y(Y1)16PY132(Y6.5)1;P9132(Y6.5) 2@P@@A ";(24);" B .@@"F05:3,60163,60163,923,923,60: ORANGE BOX_05000: PRESS RETURN0N:12:10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$;"PR#0":36860,180:D$;"RUN PART THREE (3)"0255: 1255:16368,0:24:23:"@@RETURN @@TO COECAUSE @@A = B.@@"G/5:141,96141,160:100,128180,128: DRAW AXES/7:142,110142,128:142,128162,128:142,127162,127:P: DOUBLE LINES/7:27:"@@T@@HUS, A"09:2:"@@CIRCLE@@ FORMS WHEN @@A = B@@ , AND AN"::"@@ELLIPSE @@FORMS WHEN X116:Y109:T17:(T);:T:X116:Y117:T814:(T);:T.X116:Y125:(124);:X158:Y125:(126):X116:Y133:(22):X158:Y133:(28).X116:Y140:(91);(92);(93);(94);(95);(96);(123).P/21:6:"@SR@@ADII ARE EQUAL B"@P":17000: SETTINGS ####-1:2:"A @@AND @@B@@ HAVE A PART IN PREDICTING THE"::"RADII OF THE ELLIPSE. @@W@@HEN @@A = B@@, THE MAJOR"-5:2:"AND MINOR RADII ARE ALSO EQUAL.@@T@@HIS FORMS A"-7:2:"SPECIAL ELLIPSE, A @@CIRCLE."=."@F":G IS EASIER IF THE HALF-DIAMETERS"::"ARE KNOWN. @@F@@OR CONVENIENCE WE WILL CALL THE",r19:1:"X-AXIS HALF-DIAMETER THE @@HORIZONTAL RAD-"::"IUS,@@ AND THE ONE ON THE Y-AXIS THE @@VERTICAL"::"RADIUS.@@",|5000: PRESS RETURN-N:255:B10:IAMETERS LIE ON THE X AND Y AXES."+TX90:Y62:"@F:*)('&%$#":X90:Y70:"= !":X90:Y78:"- 9":X90:Y86:"012345678@S"+^5:121,52121,108:80,78160,78+cX165:Y74:"X":X126:Y51:"Y"+ePW,h15:1:"@@S@@KETCHIN 9":17:X90:"012345678@S"I*X160:Y116:"MINOR":121,104121,135b*"5000: PRESS RETURN*@N:255:B9:"@P": SETTINGS #######&+J2:1:"A@@LL ELLIPSES FORMED BY @@A@@X@U/ + @@B@@X@U/ = @@C@@"::"ARE CENTERED ON THE ORIGIN, AND THEIR"::"D"@S@@HYPERBOLA";(13);" 2 @LPARTS"*%Pq%11:30:"@SWHILE";:13:6:"@LTHE @HPARABOLA@L HAS ONLY @HONE@L."%15:25:16215:HP$: PARABOLA%7:185,105185,158:154,132217,132: 2ND AXES %21:24:"@H@SPARABOLA";(13);" 1 @LPART"&50@HA@L HYPERBOLA CAN BE DIS-"$7:2:"TINGUISHED FROM A PARABOLA BY REMEM-"::"BERING THAT A @@HYPERBOLA@@ ALWAYS HAS @@TWO@@"::"PARTS, OR 'MORE THAN NORMAL',"$16210:14:3:"@F";HP$$7:7,13298,132:53,10453,158: WHITE AXES#%21:4:YPERBOLA":3:219,142211,100188,75:211,100188,119N#|5000: PRESS RETURNq#N:B5:255:9998:"@P":X(0)#1:1:"T@@HE WORD '@@HYPERBOLA@@' COMES FROM THE":3:2:"@@G@@REEK PREFIX '@@HYPER@@', MEANING 'MORE"::"THAN NORMAL'.";#P$" FORMS A @@HYPERBOLA.";(3);"I@@T IS FORMED WHEN A @@DOUBLE CONE@@...."f"T9:7:HP$: PLAIN HYPERB."Y19:7:"@SDOUBLE";:8:(13);"CONE@@""[P"^5:35:"@L@SIS";:2:(3);"@LCUT PERPENDICULAR TO ITS BASE.""h9:23:HCUT$5#r19:32:"@H@SH74:Y141:"@@C":X174:Y151:"B@@":7:172,150181,150O!5000: PRESS RETURNr!@N:B4:255:9999:"@P":X(0)!E16200: INIT HP$!F16205: INIT HCUT$G"J2:2:"I@@F @@A@@ AND @@B@@ HAVE OPPOSITE SIGNS AND";(3);"@@C@@ ";(24);" 0, THE EQUATION::"ORIGIN, WHOSE RADII ARE:"f 16:4:"@0@@H@@ORIZONTAL (X-AXIS) = ";:X178:Y116:N%1:NY2:9990 X187:Y117:"@@C":X187:Y127:"A@@" 7:185,126194,126: UNDERLINE 19:4:"@@V@@ERTICAL (Y-AXIS) = ":X165:Y140:N%1:NY2:99906!X14579,25: BOX48:1:"WHEN @@A ";(24);" B@@"i5:35,5181,5181,6735,6735,51: 2ND BOX 8:15:"AND @@A, B, C > 0@@"5:123,51213,51213,67123,67123,51: 3RD BOX 11:1:"@PGRAPHS AS AN @@ELLIPSE@@ WITH CENTER AT THE".".X82:Y124:N%1:NY2:9990: 2ND SQRT N"@@":4500: TRY ANOTHER?bA$"Y"įN:850xN:B3:255:9999:"@P":X(0)1:2:"W@@E NOW KNOW THAT ANY EQUATION"5:13:"@0@@A@@X@U/ + @@B@@Y@U/ = @@C@@"5:79,25177,25177,4579,$::"OR ";:X19:Y93:"@@";:N%1:NY2:9990cX28:Y93:"C":X28:Y101:"A@@":7:26,10035,10013:7:". @@T@@HE VERTICAL":15:1:"(Y-AXIS) RADIUS IS"17:1:RAD$;" OR "Y124:X91:"@@C":X91:Y134::"B@@":7:89,133100,133:17:16:""IS A CIRCLE.":12301:1:"@@S@@INCE @@A@@ AND @@B@@ ARE NOT"::"EQUAL, YOUR EQUATION"::"FORMS AN ELLIPSE WITH"::"UNEQUAL RADII."** LINE FIVE DOWN19000: DETERMINE RADII,9:1:"@@T@@HE HORIZ. (X-AXIS)"::"RADIUS IS ";RHRR:"FORM AN ELLIPSE BIG"::"ENOUGH TO SHOW HERE."~11:1:"@@P@@RESS @@RETURN@@ TO TRY":13:7:"AGAIN.":16368,0:P:800A%B%12001:1:"@@S@@INCE YOU CHOSE @@A@@ TO"::"EQUAL @@B@@,THE RADII ARE"::"EQUAL, SO THIS ELLIPSE"7:1:ETURN@@ TO SEE YOUR GRAPH."/VP:ZK%1311209[1110Y`N:12000: GRAPHING SCREENxe9500: EQUATION AT BOTTOMjK.2:H%1:11000: DRAW GRAPH t(C%)(.5((A%)))11701~1:1:"@@T@@HE VALUE YOU CHOSE"::"FOR@@ C@@ IS TOO SMALL TO":OR @@C@@ "21:29:I*T$ZA$:5500YT6ĺ"@$":21:29:(T$)2):T0:R:990vK$"POSITIVE"T%01017K$"NEGATIVE"T%01017T%0T%64T%6410171020R:21:29:"@$";(T$)2):990C%T%L23:2:"P@@RESS @@R57K$"NEGATIVE"T%0957'96021:2:"@$";K$;" @@NUMBERS ONLY!":ZS2:D:21:2:" ":19:29:(T$)2):930B%T%B%0B%5B%5ĺ"@$":19:29:(T$)2):930R 21:2:"@PE@@NTER A ";K$;" VALUE F5A%5A%0ĺ"@$":17:13:(T$)2):8805"@P"V(A%)1K$"NEGATIVE":925hK$"POSITIVE"19:2:"E@@NTER A ";K$;" VALUE FOR @@B@@"19:29:R:IT$ZA$:5500T6ĺ"@$":19:29:(T$)2):T0:930K$"POSITIVE"T%09TINE FOR AXES4:HX15:1:"X =":BTEM(B%):AEM(A%)I:JXB%0A%022610^:MXB%0A%022610n:OXB%022630y:PX22630:RXS$"-":22700:fXS$" ":X15:4:S$:X36:Y107:BTEM:7:31,11545,115:X36:Y118:AEM:;tYP1210(A37):3:P1,5P1,170(LO%11281028)256H:24582,L:24583,H:: SECOND HYPER.SET5'LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H:: CHAR SET6* 15,16,32,32,32,32,17,18,13,32,19,20,21,22,23,24,32,13,13,32,25,26,27,28,29,30,32,13,31,/ = ";C%:.4&10:1:E21,13:24:22:E19,1:d4'I1200:0:X,YX1,Y1:2:X,YX1,Y1:K:ZK%0ĂIj4'4'X(224)256(225)6:Y(226)4'7:X7N%3,Y2X2,Y2X2,Y8NY3X5,YNY81:<5'LO%(24588)256(24589):H((LO%11281028)256):L3>!V:XX:" XYYYYYZ":V1:XX:"12 34":V2:XX:"5666667":RH3H!0N3R!T3(#d32#XL1L2.5y3<#Y(XXA)BDXC3F#YY453K#XYX233P#HC:PX(XY),PY(Y)3Z#X3d#3% ** SUBROUTINE FOR EQUATION AT BOTTOM 4&%22:25:A%;"X@U/ + ";B%;"Y@UT6:2}T1$(T$,1)F2~(T1$)58(T1$)42T%((T$,3)):"@%":Q2T6:2pH((LO%2156)256):L(LO%2156)256H:24582,L:24583,H2q2XP1:X1682721:PX(P)X:PP1:X2bP1:Y168802:PY(P)Y:PP1:Y2l2@24!729!R12AINUE":5020.1(16384)194Ĺ16368,0:5050M1(16384)141Ĺ16368,0:W150201B5070,100,500,1400,1600,1700,1800,190011N:12:10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$;"PR#0":36860,170:D$;"RUN SECOND PART (2)"2|(T$)00TPX,PY:PX,P90YX0fg022:1:"@HT@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"ĺ"@$":45000"@%":A$"N"įX147:Y178:E20,1:24:21:"RETURN@@ TO CONTINUE":P:0N:"@@":255: 116368,0:255:24:9:"@HP@@RESS@@ RETURN @@TO CONTB5070,100,200,300,650,1000,1300'/P/7: FOR CIRCLE GRAPHS m/L1(((C%A%)))1:L20}/"XL1L2.2/,Y1(C(A(X2)))B/-Y104180/.Y(Y1)/6PY132(Y6.5)/;P9132(Y6.5)/@PX1497X63/JPY80PY1754185PHED, THEY ARE THE ASYMPTOTES."8./5000: PRESS RETURN.4N:12:10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$;"PR#0":36860,180:D$;"RUN FOURTH PART (4)".255:.255:16368,0:24:23:"@@RETURN @@TO CONTINUE":P.ZK%664003.!/Y159:"3":68,15776,157:20:13:"@LX"S- 5:37,14495,14495,16837,16837,144-20:16:"AND Y = -":X182:Y148:"2":X182:Y159:"3":7:180,157188,157:20:29:"@LX"- 5:141,144207,144207,168141,168141,144.*X2:Y172:"@HW@LHEN GRA:X132:Y122:NY2:N%1:9990Z,X143:Y124:"@H4":X143:Y135:"9@L":7:142,132148,132m,17:23:"@LX"t,P,17:26:"= ";(95);:X203:Y124:"2":Y135:X203:"3":201,132210,132:17:32:"@LX",P(-20:7:"Y = ";:X70:Y148:"2":X70:+P;+17:6:"Y =";:X56:Y124:"@F";"@HP";(13);"Q"j+17:10:"@S";(95);:Y124:NY2:N%1:9990+X80:Y124:"@HA";:Y135:X80:"B":7:79,13384,133+X88:Y124:"@F@HR":X88:Y132:"S@S@L"+17:15:"X"+P,17:17:"= ";(95);#*6:X143:"@HA":Y51:X143:"B"9*7:141,48147,48O*X156:Y44:"@LX"w*2:92,28170,28170,6492,6492,28*10:14:"AND GRAPH IT."*P+12:1:"@HI@LF THE EQUATION IS 4X@U/ - 9Y@U/ = 36,";CR$;"THE EQUATIONS OF THE ASYMPTOTES ARE:"20,100:120,96120,100124,1007)g5000: PRESS RETURNl)lN:B7:255:9998:"@S@P":CR$(13)(13):X(0))v1:1:"T@@O FIND THE ASYMPTOTES, SIMPLY SUBSTI-";CR$;13);"TUTE IN TO THE FORMULA")6:15:"@0@LY = ";(95);)N%1:NY2:9990: SQR.RT210,146(D3:104,12563,146D(N5:63,149210,75: BOT TO TOPd(X63,75210,149: TOP TO BOT(]22:14:"@L@04X@U/ - 9Y@U/ = 36"(b9:23:"@HA@LSYMPTOTES"(d2:152,68148,68148,82161,96:157,96162,96162,92: FIRST ARROW)e2:148,6815:3,60277,60277,1793,1793,60: BOX'&13:16:"@F@HH ";(3);" I";(3);" J";(3);"K ":13:23:" L";(3);"M ";(3);"N ";(3);" O"'+"@S"'02:136,64136,166:21,112259,112: AXES':3:104,9863,78: Q2'=169,98210,78: Q1(?169,12500: PRESS RETURNF&N:B6:255:9998:"@S@P":CR$(13)(13):X(0)&1:2:"A@@ HYPERBOLA ALSO HAS TWO @HASYMPTOTES,";CR$;" @LLINES CROSSING AT THE ORIGIN WHICH THE";CR$;" HYPERBOLA APPROACHES BUT CAN NEVER";CR$;" TOUCH, AS SHOWN HERE:"&P''N:B4:7000: SETTINGST1:1:"@H@0Y@LOU SHOULD REMEMBER THAT ANY EQUATION"4:13:"@HA@LX@U/ + @HB@LY@U/ = @HC@L":5:77,16183,16183,3877,3877,167:1:"WHEN @HA , B@L HAVE OPPOSITE SIGNS":5:35,43225,43225,6235,6235,43B1A%)1K$" X ":K2$"A"K$;"-AXIS,";(3);"SINCE THE";K$;"COEFFIC-";(3);"IENT (@H";K2$;"@L) IS THE ONE";(3);"THAT'S POSITIVE."13:1:"@HT@LHE GREEN AND PURPLE";(3);"DOTS REPRESENT THE";(3);"ASYMPTOTES."4500: TRY ANOTHERA$"Y"610MITED RANGE OF THIS";(3);"SET OF AXES."A4500: TRY ANOTHER UA$"Y"įN:610_10001:1:"@HT@LHIS IS A ROUGH GRAPH";(3);"OF YOUR EQUATION.5:1:"@HN@LOTICE THAT THE GRAPH";(3);"LIES ON THE";(A%)1K$" Y ":K2$"B"( GRAPHING SCREEN0f9500: EQUATION AT BOTTOMRk(A%)1(B%)1(C%)55890tpK.25:H%1:11000: GRAPH IT}u920(z1:1:"@P@HT@LHE VALUES YOU CHOSE";(3);"FOR THE EQUATION FORM";(3);"A HYPERBOLA THAT";(3);"CAN'T BE SHOWN ON THE";(3);"LI:R:I T$ZA$:5500F*T6ĺ"@$":20:31:(T$)2):T0:R:790a.T%0T%64T%64817j08201R:20:31:"@$";(T$)2):7904C%T%>23:2:"@HP@LRESS @HRETURN@L TO SEE YOUR GRAPH."HP:ZK%13860R840\N:12000: * * *57K$"NEGATIVE"T%0757'760{21:2:"@$";K$;" @HNUMBERS ONLY!":ZS2:D:21:2:25):18:33:(T$)2):730B%T%B%0B%5B%5ĺ"@$":18:33:(T$)2):730R 20:2:"@P@HE@LNTER A NON-ZERO VALUE FOR @HC@L"20:303A%5A%5A%0ĺ"@$":16:15:(T$)2):670T(A%)1K$"POSITIVE":725fK$"NEGATIVE"18:2:"@HE@LNTER A ";K$;" VALUE FOR @HB@L"18:33:R:IT$ZA$:5500T6ĺ"@$":18:33:(T$)2):T0:730K$"POSITIVE"T%07"X =":BTEM(B%):AEM(A%)/>JXB%0A%022610D>MXB%0A%022610T>OXB%022630_>PX22630q>RXS$"-":22700|>fXS$" ">X15:4:S$:X36:Y107:BTEM:7:31,11545,115:X36:Y118:AEM:>tYP1210(A37):3:P1,5P1,170:: AXIS OF SYMM. AXIS AND BOX IN CORNERD=*N5:151,84277,84277,176151,176151,84t=4N2:162,128272,128:210,88210,172: AXES=9N2:I1622728:I,127I,129:I:I881728:208,I212,I:I: TICK MARKS=>NX155:Y124:"X":X217:Y88:"Y"=N>HX15:1:BOLA<8J ** DETERMINE RADII? ?@HA"(3)"B C"(3)"D E"(3)"F G@S":: PARA$"@FABCDEF"(3)"GHIJKL"(3)"MN OP"(3)" QRST"(3)" UV"(3)" WXYZ"(3)"@@AB CD"(3)"E F"(3)"GHIJKL":";M?:CR$(3):HCUT$"@F@LABCD@HM"CR$"@LGHI@HNO"CR$"@LMN @HPQ"CR$"@L QR@HRS"CR$" @LUV"CR$" @LWX@HTU"CR$"@HAB VW"CR$"EHCH7:HC2(HC2)14020896X1H712:X2H74:14030O96X1H713:X2H7396Y1V811:Y2V83:5:X1,Y1X2,Y1X2,Y2X1,Y2X1,Y1:9:HC9:V1150209:IX1X2:I,Y1:N110:N:I:150309:IY1Y2:X1,I:N110:N:I9:V0:HC0:|:H?HP88:210,5210,167:2:32:"@@Y":X141:Y85:"X": DRAW AXES U8."@P": PROP.SPC.8/ZY8827:208,ZY213,ZY:ZY:ZY881677:208,ZY213,ZY:ZY8/7:ZX2102778:ZX,86ZX,89:ZX:ZX2101478:ZX,86ZX,89:ZX8/821:1:(15);"F":9611028*7+PYPYH%:P9P9H%:PX,PY:PX,P917+XK7+J11030,11031:11035m7+IL3:LL4:SK:XILS:110107+IL4:LL2:S.08:110107+H%0:7. SUBROUTINE FOR AXIS & BOX7.5:137,1277,1277,177137,177137,1: ORANGE BOX ?8.6:147,88273,37,32,32, 38,39 "6*J0:7_6*P10:L1(((C%A%)))1::L2(L1):L3.666L1:L4.666L2s6*S.08:IL1:LL36+JJ1:XILS6+Y1(C%(A%(X2)))B%6+O886 +Y10110286 +Y(Y1):PY88(Y7):P988(Y7):PX1488X63:H07 +PY1PY175G THEM WOULD PRODUCE THE";CR$;"TWO STRAIGHT LINES."L-5000: PRESS RETURNw- * * * * PUT SCREEN 40 HERE IF NEEDED-N:12:10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$"PR#0":36860,180:D$"RUN PART FIVE (5)"-255:.255:16368,0:24:9;,15:15:"X":5:45,100113,100113,13245,13245,100b,15:19:"AND Y = -";:Y105:9990,Y107:X198:"3":Y123:X198:"3":190,119206,119,15:32:"X ,",5:151,100229,100229,132151,132151,100: 3RD BOX3-18:2:"AND GRAPHIN240,32240,56174,56174,32: 1ST BOX+|9:2:"AND SUBSTITUTE IN IT THE VALUES FOR @HA@L AND";CR$;"@HB. W@LE WOULD COME UP WITH THE TWO EQUA-";CR$;"TIONS"+15:8:"@LY@L = ";:Y105:NY1:N%1:9990,Y107:X82:"3":Y123:X82:"3":3:74,11990,11 SETTINGSO*J1:8:"T@LO GRAPH THIS EQUATION...";CR$;5);"3X@U/ - 9Y@U/ = 0"Y*O6000*T6:2:"@HW@LE WOULD TAKE THE FORMULA Y = ";(95);:Y36:NY2:N%1:9990*^Y36:X218:"@HA":Y46:X218:"B@L":3:216,44224,44*h6:34:"X"%+r2:174,32";CR$;(13);" Y = ";(95);:Y76:NY2:N%1:9990e)Y76:X52:"@HA":Y85:X52:"B@L":3:50,8358,83v)11:10:"X")2:4,7280,7280,964,964,72)10:14:"AND GRAPH THE RESULTING";CR$;"TWO EQUATIONS.")"5000: PRESS RETURN *@N:B9:7000:(5000: PRESS RETURN3(N:B8:7000: SETTINGS(2:2:"W@LHEN GRAPHING THE LINES, YOU FOLLOW THE";CR$;"SAME PROCEDURE AS FOR GRAPHING THE ASYMP-";CR$;"TOTES OF A HYPERBOLA. @HS@LUBSTITUTE THE"/)8:2:"VALUES OF @HA@L AND @HB@L INTO THE FORMULAOPPOSITE IN SIGN, IT COULD DES-";CR$;"CRIBE EITHER A HYPERBOLA OR TWO LINES"'7:1:"THROUGH THE ORIGIN. @HT@LO TELL WHICH, JUST";CR$;"LOOK AT @HC@L. @HI@LF @HC = 0, @LIT'S TWO LINES";CR$;"THROUGH THE ORIGIN. @HA@LNYTHING ELSE IS";CR$;"A HYPERBOLA."0203,169:161,143245,143: 2ND AXES e&Z3:175,125231,161:175,161231,125: TWO LINES AT ORIGIN|&d23:28:"@HC = 0"&n5000: PRESS RETURN&x1:1:E40,13:24:1:E40L'1:1:"@HS@LO WHEN YOU SEE AN EQUATION WHERE @HA@L AND";CR$;"@HB@L ARE 1:59,11059,169:21,14398,143>%>23:7:"@HC ";(24);" 0"H%A6000%F8:1:"@HB@LUT WHEN @HC@L IS ZERO, THAT SHOWS THAT THE";(3);"CUT WAS MADE IN THE EXACT CENTER, SO TWO";(3);"STRAIGHT LINES THROUGH THE ORIGIN ARE";(3);"FORMED."&&P1:203,11O, THE CUT IS MADE OFF";(3);"OF THE CENTER. @HT@LHAT FORMS A HYPERBOLA."}$(18:7:"@F";(28);(29);(3);(30);(31);"@S"$-18:10:"@F";(23);(24);(3);(25);(26);"@S"$23:47,13629,122:47,15129,166$73:71,13689,122:71,15189,166 %<LINES-";(3);"@LHAPPENS TO BE IN";(13);" EXACT CENTER"W#"@S":5000: PRESS RETURNs#N:B7:7000: SETTINGSJ$1:1:"T@LHE FACT THAT THE CONE IS CUT IN ITS CENTER";(3);"IS SHOWN BY THE VALUE OF @HC@L. @HW@LHEN @HC@L IS";(3);"ANYTHING BUT ZERR$;"ARE A SPECIAL CASE OF A HYPERBOLA."1"6000I"8:6:16205:HCUT$]"CR$(13)(13)"18:2:"@S@H HYPERBOLA-";(3);"@LNOT CUT THROUGH";(13);" EXACT CENTER""6000"8:25:16210:9998:HP$:9999:8:27:H2$8#18:21:" @S@HTWO !y9999!}"@%"E!~16210:11:24:9998:HP$:11:26:9999:H2$_!"@S": STANDARD FONTx!5000: PRESS RETURN!N:B6:7000:9998: SETTINGS'"1:1:"J@LUST AS A CIRCLE IS A SPECIAL CASE OF";CR$;"AN ELLIPSE, TWO LINES THROUGH THE ORIGIN";COSITE SIGNS, AS IN A";CR$;"HYPERBOLA, BUT @HC@L = 0, THE GRAPH FORMS";CR$;"@HTWO STRAIGHT LINES THROUGH THE ORIGIN." `7:1:"@HT@LHEY ARE FORMED WHEN A DOUBLE CONE..." j16200:11:8:HP$ o6000!t9:1:"@S@L@PIS CUT THROUGH ITS EXACT CENTER.":87,107155,107155,13687,13687,107C815:24:", AND LOCATED"B19:1:"ON THE AXIS OF THE VARIABLE (X OR Y) WITH";CR$;"THE POSITIVE COEFFICIENT."G5000: PRESS RETURNLN:B5:7000:9998: SETTINGSt V1:1:"I@LF @HA @LAND @HB@L HAVE OPP0:9:"AND @HC ";(24);" 0":5:99,66149,66149,8699,8699,6613:1:"@PG@LRAPHS AS A @HHYPERBOLA@L WITH ASYMPTOTES";CR$;"DESCRIBED BY Y=";(95);:NY2:N%1:9990$15:19:"@HA":19:Y122:"@HB@L":7:123,120133,120&.Y116:21::"@LX":53:161,96161,168K157,103161,96165,103:157,161161,168165,161RP5:19:"@HT@LHEY'RE PARALLEL";:7:3:"BECAUSE ONE IS JUST THE OPPOSITE OF";CR$;"THE OTHER."5000: PRESS RETURNN:B6:7000: SETTINGS"@0"(1:1:"1:3:"S@LINCE WE CAME UP WITH TWO DIFFERENT";CR$;"STRAIGHT LINE EQUATIONS,"w"@0":13:11:"X=-2":13:26:"X=2"3:25:"@PTWO LINES"5:3:"WILL BE PRODUCED."3:107,96107,1683:103,103107,96111,103:103,161107,168111,161= -2 ."@154,164210,164210,180154,180154,164: 3RD BOX Y5000: PRESS RETURNuN:B5:7000: SETTINGS2:63,134217,134:134,98134,170:I6421814:I,133I,135:I:I9817012:132,I137,I:I12:20:"@LY@H":17:33:"@LX@H"N ..." aP.f18:17:"X = ";(95);" 2 ."hp2:106,131168,131168,148106,148106,131: 1ST BOXouPz20:1:"@HF@LROM THIS WE GET THE TWO EQUATIONS";CR$;8);"X = 2"|2:50,16498,16498,18050,18050,164: 2ND BOX~22:18:"AND X 210,88210,172: AXESf99N2:I1622728:I,127I,129:I:I881728:208,I212,I:I: TICK MARKS9>NX155:Y124:"X":X217:Y88:"Y"I @F*"(127)(3)"+,"(3)"-."(3)"/"(91)(3)(92)(93)(3)(94)(95)(3)8T?H2$H2$"@LZ"(123)(3)(124)(125)(3)(126)8V?8 N TO DRAW AXIS AND BOX IN CORNER8*N5:151,84277,84277,176151,176151,8494N2:162,128272,128:UT$"@F@LABCD@HM"CR$"@LGHI@HNO"CR$"@LMN @HPQ"CR$"@L QR@HRS"CR$" @LUV"CR$" @LWX@HTU"CR$"@HAB VW"CR$"E XY"CR$"GHIZ@S":: CUT CONE 7R?HP$"@F@LABC"(3)"GH"(3)"MN"(3)" Q"(3)" "(3)" W"(3)"@HAB"(3)"E"(3)"GH"V8S?H2$"X1H712:X2H74:14030066X1H713:X2H73k66Y1V811:Y2V83:5:X1,Y1X2,Y1X2,Y2X1,Y2X1,Y1:6H?HP$"@F@LABCDEF"(3)"GHIJKL"(3)"MN OP"(3)" QRST"(3)" UV"(3)" WXYZ"(3)"@HAB CD"(3)"E F"(3)"GHIJKL":7M?CR$(3):HC5210,167:2:32:"@@Y":X141:Y85:"X": DRAW AXES M5."@P": PROP.SPC.5/ZY8827:208,ZY213,ZY:ZY:ZY881677:208,ZY213,ZY:ZY5/7:ZX2102778:ZX,86ZX,89:ZX:ZX2101478:ZX,86ZX,89:ZX5/56HCH7:HC2(HC2)14020664+J11030,11031:C%011035)4+11055K4+IL3:LL4:SK:XILS:11010f4+IL4:LL2:S.25:110104+:C%0C%0:J0:3:110054/+4. SUBROUTINE FOR AXIS & BOX4.5:137,1277,1277,177137,177137,1: ORANGE BOX 75.6:147,88273,88:210,3*P10:L18:L2(L1):L3.666L1:L4.666L2@3*S.25:IL1:LL3S3+JJ1:XILSm3+Y1(C%(A%(X2)))B%v3+O883 +Y10110273 +Y(Y1):PY88(Y7):P988(Y7):PX1488X63:H03 +PY1PY175110273+PYPYH%:P9P9H%:PX,PY:PX,P93+X2X2,Y8NY3X5,YNY81:2'LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H:: HYP CONE SET2'LO%(24588)256(24589):H((LO%2156)256):L(LO%2156)256H:24582,L:24583,H:: SECOND HYPER SET2*J0:7,### 1b51% ** SUBROUTINE FOR EQUATION AT BOTTOMa1&%22:25:A%;"X@U/ + ";B%;"Y@U/ = ";C%:1&10:1:E21,13:24:22:E19,1:1'I1200:0:X,YX1,Y1:2:X,YX1,Y1:K:ZK%0ĂI1'1'X(224)256(225)6:Y(226)2'7:X7N%3,Y2X2,Y MOMENT PLEASE...":D$(13)(4):D$"PR#0":36860,170:D$;"RUN PART THREE (3)"b0|(T$)0T6:r0}T1$(T$,1)0~(T1$)58(T1$)42T%((T$,3)):"@%":0T6:0p16368,0:P:1XCA$(3):CR$(13)(13):9999:"@S@P":255: SETTINGS ####E":P:/N:"@@":255:_/16368,0:255:24:9:"@HP@@RESS@@ RETURN @@TO CONTINUE":5020/(16384)194Ĺ16368,0:5050/(16384)141Ĺ16368,0:/5020/B5070,100,300,600,1000,1100,1200,1300,1500,1600/N0N:12:10:"@HO@LNE23:"@@RETURN @@TO CONTINUE":P0.ZK%6640036.k.B100,100,300,600,1000,1100,1200,1300,1500,1600q..22:1:"@HT@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"ĺ"@$":4500/"@%":A$"N"įX147:Y178:E20,1:24:21:"RETURN@@ TO CONTINUAND";CA$;"@HC@L = 0, THE EQUATION DESCRIBES A SINGLE";CA$;"@HPOINT @LAT THE ORIGIN."r*T6000: DRAW GRAPHING BOX+^8:1:" 2X@U/ + 3Y@U/ = 0";CR$;"@HO@LNLY THE VALUES X=0";CR$;"AND Y=0 SATISFY THIS";CR$;"EQUATION, SO THE POINT";CR$;"IS AT THE ORIGIN) THROUGH THE ORIGIN. @HI@LT EITHER";CR$;"LIES ON THE X-AXIS OR ON THE Y-AXIS, AS";CR$;"DETERMINED BY THE VARIABLE IN THE EQUA-";CR$;"TION.")"5000: PRESS RETURN)@N:B10:7000: SETTINGST*J2:2:"@HI@LF @HA@L AND @HB@L BOTH HAVE THE SAME SIGN, 7,3777,16: 1ST BOX i(7:1:"WHEN @HA@L OR @HB@L = 0":43,43123,43123,6043,6043,43: 2ND BOX(7:20:"AND @HC@L = 0":161,43207,43207,60161,60161,43: 3RD BOX )10:1:"@PGRAPHS AS @HTWO COINCIDENT PARALLEL LINES";CR$;"(@LONE LINEDOES";CR$;"90963X@U/ = 0 , SINCE SOLVING FOR X ELIM-";CR$;"INATES THE COEFFICIENT."m'5000: PRESS RETURN 'N:B9:7000: SETTINGS'1:7:"S@LO ANY EQUATION OF THE FORM"'4:13:"@0@HA@LX@U/ + @HB@LY@U/ = @HC@L"(5:77,16183,16183,377S";CR$;"Y@U/ = 0 GRAPHS ON THE Y-AXIS"B&5000: PRESS RETURNh&13:1:E40,5:24:5:E30: ERASE&14:4:"@P@HT@LHE VALUE OF @HA@L OR @HB@L MAKES NO DIFFER-";CR$;"ENCE IN THE LOCATION OF THE LINE."S'18:4:"X@U/ = 0 GRAPHS THE SAME LINE AS ZERO, THE GRAPH WILL BE OF @HTWO COINCIDENT";CR$;"PARALLEL LINES (@LONE LINE) THROUGH THE";CR$;%"ORIGIN. @HT@LHEY (IT) ALWAYS LIES ON THE AXIS";CR$;"OF THE VARIABLE (X OR Y) IN THE ORIGINAL";CR$;"EQUATION.")&14:4:"X@U/ = 0 GRAPHS ON THE X-AXINE LINE ON":3:4:"THE X-AXIS. @HT@LHIS SPECIAL CASE IS AN";CR$;"ILLUSTRATION OF THE NEXT TYPE WE'RE";CR$;"GOING TO DISCUSS..."$Z5000: PRESS RETURN$xN:B8:7000: SETTINGS_%1:1:"W@LHEN EITHER @HA@L OR @HB@L IS ZERO, AND @HC@L IS ALSO";CR$;"EN WE GRAPH Y@U/ = 0..."x#(5:15,124141,124:19,12115,12419,127:137,121141,124137,127: CHANGE X AXIS TO ORANGE#216:23:"Y@U/ = 0"#<5000: PRESS RETURN#F1:1:E40,7:24:1:E35:"@P": ERASE$P1:1:"@L...OUR TWO LINES MERGE INTO O137,103:137,145141,148137,151: ARROWSB"Y96:22:"Y@U/ = 4"[" 5000: PRESS RETURN"1:1:E40,7:24:1:E35:"@P": ERASE#1:1:"@HI@LT'S CLEAR THAT AS @HC@L IS DECREASING, OUR";CR$;"LINES ARE COMING CLOSER TOGETHER.";CR$;"@HF@LINALLY, WH!1:1:E37,7:24:1:E35:"@P"!1:1:"@HD@LECREASING @HC@L STILL FURTHER AND GRAPHING";CR$;"Y@U/ = 4 GIVES TWO LINES EVEN CLOSER";CR$;"TOGETHER."!3:14,100141,100:14,148141,148)"19,9714,10019,103:19,14514,14819,151:137,97141,100 9 AND GRAPHING Y@U/ = 9";CR$;"GIVES TWO LINES AT Y=3 AND Y= -3 ."g 6:14,88141,88:14,160141,160 19,8514,8819,91:19,15714,16019,163:137,85141,88137,91:137,157141,160137,163: ARROWS Y83:22:"Y@U/ = 9" 5000: PRESS RETURN!:14,172141,172u19,7314,7619,79:136,73141,76136,79:19,16914,17219,175:137,169141,172137,175: ARROWS10:22:"Y@U/ = 16"5000: PRESS RETURN1:1:E38,7:"@P": ERASE24:1:E40:"@P"B 2:1:"@HD@LECREASING @HC@L TOLUE OF @HC@L."vt2:76,6476,184:6,124146,124:I614614:I,122I,126:I:I6418412:74,I78,I:I: AXES ~9:13:"Y":15:2:"X"P5:1:"@HG@LRAPHING Y@U/ = 16 GIVES TWO LINES AT";CR$;"Y = 4 AND Y = -4 ."1:14,76141,76 PRESS RETURN*LN:B7:7000: SETTINGSV2:2:"B@LEFORE GOING ON, LET'S STUDY THE LAST";CR$;"TYPE OF EQUATION SLIGHTLY FURTHER..."`5000: PRESS RETURNjN:7000:1:1:"L@LET'S GRAPH SEVERAL EQUATIONS, WHERE";CR$;"NOTHING CHANGES BUT THE VAHAVE";(13);2);"LIKE SIGNS"K873,67187,67187,9373,9373,67: 3RD BOXB14:1:"WILL FORM @HTWO DISTINCT PARALLEL LINES.";CR$;"S@LUCH AN EQUATION WILL ONLY HAVE ONE";CR$;"VARIABLE, SINCE THE OTHER HAS A ZERO"D20:12:"COEFFICIENT."G5000:@HT@LHEREFORE, ANY EQUATION OF THE FORM"T4:13:"@HA@LX@U/ + @HB@LY@U/ = @HC@L"|5:77,16175,16175,3877,3877,167:6:"WHEN @HA@L OR @HB@L = 0"85,45165,45165,6085,6085,45: 2ND BOX$Y76:7:"AND".10:12:"THE OTHERS z#?    ŠŮԠ!ŮԠ"ĠҮԠٮԠ ĠԠ $ ĠԠ5ԠŠ8ȠԠ3ԠŠ9ȠԠǠŮԠŮԠϠ îàϠ!à ڮ٠Šڮ٠Šˠ(ԠŠ45000: PRESS RETURN2.N:B11:7000: SETTINGS].1:7:"S@LO ANY EQUATION OF THE FORM".4:13:"@0@HA@LX@U/ + @HB@LY@U/ = @HC@L".&5:77,16179,16179,3677,3677,16: 1ST BOX/07:1:"WHEN @HA,B @LHAVE";:8:9:"THE SAME";(13);" SIGNE SAME";CA$;"SIGN, JUST ONE AND";CA$;"ONLY ONE CAN'T BE";CA$;"NEGATIVE. @HT@LHEREFORE,";CA$;"BOTH TERMS MUST BE";CA$;-"ZERO TO SATISFY THE";CA$;"EQUATION."-P-19:21:"@HS@LO THE ONLY SOLUTION";CA$;"SET IS (0,0), FORMING";CA$;"THE POINT.".ERO..."$,X188:X297:Y165:15000x,16:1:"UNLESS (A) ONE OF";CR$;"THEM IS NEGATIVE, OR";CR$;"(B) BOTH ARE ZERO.",4000: PRESS RETURN,10:1:E20,13:23:20:E20,2:"@P": ERASEu-10:1:"@HS@LINCE @HA@L AND@H B@L BOTH";CA$;"MUST HAVE TH."6+h3:201,95203,95203,97201,97201,95: POINT O+r4000: PRESS RETURN+|10:1:E20,10:23:20:E20,2:"@P": ERASE+10:1:"@HT@LHAT'S BECAUSE THE";CR$;"@HSUM@L OF TWO TERMS...";CR$;+X112:X273:Y165:15000,14:1:"CAN NEVER BE ZLEASE...":(13);(4)"RUN PART ONE (1)"DOME DAM-";CR$;_"AGED.";CR$;"@HW@LITHIN ABOUT 30 SECONDS, THE PROGRAM WILL";CR$;"CONTINUE."24:3:"@HP@LRESS @HRETURN@L TO START THE PROGRAM..."P:ZK%13(ZK%)"B"200(ZK%)"B"1201000'N:12:10:"@HO@LNE MOMENT PTHE COMPUTER";CR$;"WILL COME ON. @HD@LON'T PANIC; THE COMPUTER";CR$;"IS JUST LOADING IN THE NEXT PART OF THE";CR$;"PROGRAM. @HP@LLEASE DON'T PRESS @HRESET@L OR TRY";CR$;"TO TAKE THE DISK OUT OF THE DRIVE AT THIS";CR$;"TIME, BECAUSE THE DISK MIGHT BECG SIMILAR, AT THE BOTTOM OF THE";(13);(13);"SCREEN."f24:10:"@HP@LRESS @HRETURN@L TO CONTINUE"P:ZK%13(ZK%)"B"151(ZK%)"B"74DN:"@P":2:1:"@HP@LERIODICALLY, THE PROGRAM WILL STOP, AND";CR$;"THE DISK DRIVE BY THE SIDE OF (13);"TO PRESS @HRETURN@L. @HA@LFTER YOU DO, MORE OF";(13);(13);"THE SCREEN WILL APPEAR. @HB@L WILL NOT WORK";(13);(13);6"HERE; IT ONLY WORKS WHEN YOU SEE THE";(13);(13);"STATEMENT '@HP@LRESS @HRETURN@L TO CONTINUE', OR";(13);(13);"SOMETHINRY GOOD!":60 xN:"@P":2:1:"@HS@LOME SCREENS ARE DIVIDED INTO ONE OR";(13);(13);"MORE SEGMENTS. @HI@LF YOU'RE LOOKING AT A";(13);(13);"SCREEN AND NOTHING SEEMS TO BE HAPPENING,";(13);(13);"THE COMPUTER IS PROBABLY WAITING FOR YOU";(13);@LYOU CAN PRESS @HRETURN@L TO GO FORWARD TO";(13);(13);"THE NEXT SCREEN, OR @HB@L TO GO BACKWARDS";(13);(13);"TO THE LAST SCREEN." i24:10:"@HP@LRESS @HRETURN@L TO CONTINUE" nP:ZK%13(ZK%)"B"110 s(ZK%)"B"įN:"@P":1:1:"@HV@LER OF";(13);(13);"'SCREENS', SIMILAR TO PAGES IN A BOOK." P6:1:"@HT@LO FLIP THROUGH THEM, USE THE @HRETURN@L";(13);(13);"AND @HB@L KEYS. @HF@LOR EXAMPLE, WHEN YOU SEE" Z10:1:"THE STATEMENT '@HP@LRESS @HRETURN@L TO CONTINUE'," d12:1:"ENCE @HF@LOUNDATION @HG@LRANT @HN@LO. @HSER-8103997." >20:1:"@HW@LOULD YOU LIKE INSTRUCTIONS FOR USING";CR$;9);"THIS PROGRAM?" FP:(ZK%)"N"1000 G(ZK%)"Y"70 JCR$(13)(13): KN::"@P":2:1:"@HT@LHIS PROGRAM CONSISTS OF A NUMBEROGRAM";CR$;"DESIGNED TO TEACH THE RECOGNITION OF THE";CR$;"EQUATIONS OF CONIC SECTIONS, AND WAS";CR$;"ORIGINATED BY @HJ.C. H@LOLTON.";CR$;CR$;5 ="@HI@LT WAS WRITTEN AND PROGRAMMED BY A COL-";CR$;"LEGE STUDENT, WITH THE AID OF @HN@LATIONAL";CR$;"@HS@LCI)  HELLO (DON'T TOUCH)2 GREETING PROGRAM> D$(4)cD$"BLOAD PIC.CAJC LOGO, A$2000"16297,0:16302,0:16304,0(16368,02(4)"BRUN ENPACK"7::N:"@P":CR$(13)(13) <3:1:"@HW@LELCOME TO @HCONICS. CONICS @LIS A P     ת׿תժ߿߻ߪ׿ߪתժߪժߪժߪ߮ߪߪժ׿תժ߿߾ߪ׿ߪպתժߪߪ߿ժߪժߪ߯ߪߪ߮׿ߪժ߿߾׿תժݯߪժժժժժժժתժ߿߯תկ׿ߪժ߿߾׿תժݿת@ߪ߮2ժ           n&n;ȱn/ȱ%$xo n0 ȱ0ȱxpȱo-%ox= noȥo`  w x`oLn.@& $< >,.?: ; ` 8`2Fa b6uuWhwwwwI  mLml n nLl m=Ll mLml m n x m&Lml= mLl mJ  mLml n mLm n mLem m m& nLrlLl x m&Lml= mLml[A0 ``x$= no nd0)ȱ0ȱ0(R0杩HphphoDh )phh elLIlphh8pȩXoDОƝCqȑop`& n nX&`Lml n m& n= m `` HAheh8& &i``枩x m n m mI0) LjLZj-h-hB!&,h0)? ,h)&,h&A-h0  JJ-h&',h0%% 0杹,h&& 'yNh'Х&&C ppp`'pLalppppp 4fnEoDmD,h07H)?!0еH el@hphh@LiL$i nLalLkC&,h(g@e@&'&ȱȱJI&@'0:,h3 ,Nh%0 Nh,h& @,hNhhLj'0",h  0 0,h&,h' nLiLj<>ŝ ढ़pLalȹo msLhixpn ȹo >гclIwBmГAe@8+h *hЪ0CCȥȄ@ nLi nȐLh!h `mIBAC@n(gklȥȑhhh hLf &ȑȑ`湥ff ` e` 4fEo` e o8EopEȥoȥp`Z jfHȱȱh`څijkl+уȥуiLvfi愠`H HHHm8knl   mimnki` f :d0V 80H    e e he f: 0Ő f : ,hhL` ` b f a f a%%:! ,Ƙ  jf ȱL]e jfȄ ᥠ L`eZ jf) I hfȱ`pZS jf68 ȱ pȱnpnpnpnp𘪠`)7`ɀ8` E` a{I mLd`I ɀ "ɎLdɏɆLdɇɐЍ >p)pp eFL` e e e e e es f mxL`: D eC, eD,L` yqqHHH$H%HDC q qLc yh%h$hhhL` e΄Ϣ($,L` e % c둃L` c%Lc hfȱ08``[A0{a0o VfEq, ppLgb d pdpEEEqiE hHH eh ehi ep eppp p fL` hf Ky hfȱii f eڢn f e eZT jfp0ɯ fLU`pppp fpp0 f:T" d fLb"< pdo, f%"!H mv f nf%Eȱȱ pd oLTaEL7a:`:<~:~:~mxq111182COPYRIGHT 1982 COMPUTER TEACHING CORP.J``LM`ƹƸ | f maL aeLKcoLai dLbm }L`r@k {Lcp d {LbtxLcyLcsLcuLcn exL'cd d {_ ` `l `` : f`          Y17511028/<+PYPYH%:P9P9H%:PX,PY:PX,P96<+XP<+J11030,11031:11035r<+IL3:LL4:SK:XILS:11010<+IL4:LL2:S.25:11010<+H%0:<. SUBROUTINE FOR AXIS & BOX<.5:137,1277,1277,177137,177137,1: ORANGE BOX D=.6:147,88L(LO%11281028)256H:24582,L:24583,H:6;*J0:7d;*P10:L18:L2(L1):L3.666L1:L4.666L2x;*S.25:IL1:LL3;+JJ1:XILS;+Y1(C%(A%(X2)))B%;+O88; +Y1011028; +Y(Y1):PY88(Y7):P988(Y7):PX1488X63:H0 < +PY1P@U/ = ";C%:0:&10:1:E21,13:24:22:E19,1:f:'I1200:0:X,YX1,Y1:2:X,YX1,Y1:K:ZK%0ĂIl:':'X(224)256(225)6:Y(226):'7:X7N%3,Y2X2,Y2X2,Y8NY3X5,YNY81:+;'LO%(24588)256(24589):H((LO%11281028)256):0141,53.92:202,56202,136:152,96256,96T9Y92:X260:"@LX":Y56:X207:"Y"92:I561368:200,I204,I:I:I15225610:I,95I,97:I99XCA$(3):CR$(13)(13):9998:"@S@P":255: SETTINGS9b9% :&%22:25:A%;"X@U/ + ";B%;"Y,1800,1900,21008w8N:12:10:"@HO@LNE MOMENT PLEASE...":D$(4):D$;"PR#0":36860,170:D$"RUN FOURTH PART (4)"8|(T$)0T6:8}T1$(T$,1)8~(T1$)58(T1$)42T%((T$,3)):"@%":8T6:8p9z5:141,53267,53267,140141,1424:21:"RETURN@@ TO CONTINUE":P:77N:"@@":255:{716368,0:255:24:9:"@HP@@RESS@@ RETURN @@TO CONTINUE":50207(16384)194Ĺ16368,0:50507(16384)141Ĺ16368,0:750208B5070,100,500,700,800,900,1000,1100,1400,1500,1600::6255:16368,0:24:23:"@@RETURN @@TO CONTINUE":P@66B100,100,500,700,800,900,1000,1100,1400,1500,1600,1800,1900,21006622:1:"@HT@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"ĺ"@$":4500#7"@%":A$"N"įX147:Y178:E20,1:"AND"15R12:8:"@HC@L HAS THE OPPOSITE SIGN ,"X5W43,84217,84217,10443,10443,845\15:7:"THE GRAPH IS THE @HNULL SET@L."5f50005pN:12:10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$;"PR#0":36860,180:D$;"RUN SIXTH PART (6)"6255U491:11:"@0@HS@LO IN ANY EQUATION";CR$;(13);" @HA@LX@U/ + @HB@LY@U/ = @HC@L ,"}4>5:77,16179,16179,3777,3777,164C7:1:"WHEN @HA,B @LHAVE THE SAME SIGN, OR":8:10:"ONE OF THEM IS ZERO"4H35,44231,44231,6835,6835,445M10:17:1:"@HB@LUT IT HAS NO REAL NUMBER SOLUTION, SINCE";CA$;"@HSQUARED@L TERMS..."l3X198:X2147:Y1138:15000319:17:CA$;"CANNOT EQUAL A NEGATIVE":22:1:"NUMBER."3X1167:X2182:Y1138:1500035000: PRESS RETURN34N:B13:7000: SETTINGST (0")27:139,109132,121: CROSS OUTQ215:21:").@HH@LERE'S AN EXAMPLE:"q217:15:"X@U/ + Y@U/ = -1"219:4:"@HA@L AND @HB@L ARE BOTH POSITIVE, AND @HC@L";CR$;11);"IS NEGATIVE."25000: PRESS RETURN219:4:E34,6:"@P"M319:"-1X152:X2130:Y154:HC2:15000: LINEg1Y52:X136:"@HAND@L":X1158:X2252:Y154:HC2:1500019:9:"2). @HC@L HAS SIGN OPPOSITE";CA$;" THAT OF @HA@L AND @HB@L,"213:1:"ITS GRAPH DOES NOT EXIST; TECHNICALLY,";CR$;"IT'S THE @HNULL SE"0b5000: PRESS RETURN70lN:B12:7000: SETTINGSl0v1:1:"F@LINALLY, IF YOU SEE AN EQUATION WHERE"0{2:52,20252,20252,9252,9252,20: BOX14:9:"@01). @HA @LAND @HB @LHAVE THE SAME";(13);" SIGN, OR ONE OF THEM";(13);" IS ZERO,"0/:49,42123,42123,7649,7649,42: 2ND BOXM/D8:20:"AND @HC@L = 0"/N161,50207,50207,69161,69161,50: 3RD BOX0X12:1:"@PGRAPHS AS A @HPOINT AT THE ORIGIN, @LSINCE";CR$;"THE ONLY VALUES WHICH SATISFY IT ARE";CR$;" X = 0 AND Y = 0 .dTB|`{} _\@[]  ~ ^'LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H:`*J0:7*P10:L18:L2(L1):L3.666L1:L4.666L2*S.25:IL1:LL3+JJ1:XILS+Y1(C%(A%(X2)))B%+O88 +Y1011028 +Y(Y1):PY88(Y7)R EQUATION AT BOTTOM@&%22:25:A%;"X@U/ + ";B%;"Y@U/ = ";C%:d&10:1:E21,13:24:22:E19,1:'I1200:0:X,YX1,Y1:2:X,YX1,Y1:K:ZK%0ĂI''X(224)256(225)6:Y(226)'7:X7N%3,Y2X2,Y2X2,Y8NY3X5,YNY81:U1,53*2:202,56202,136:152,96256,96PY92:X260:"@LX":Y56:X207:"Y"2:I561368:200,I204,I:I:I15225610:I,95I,97:Id16368,0:P:XCA$(3):CR$(13)(13):9998:"@S@P":255: SETTINGSb% ** SUBROUTINE FO10:"@HO@LNE MOMENT PLEASE...":D$(13)(4):D$;"PR#0":36860,170:D$;"RUN PART FIVE (5)"n|(T$)0T6:~}T1$(T$,1)~(T1$)58(T1$)42T%((T$,3)):"@%":T6:p*** GRAPHING BOX FOR B=10z5:141,53267,53267,140141,14014:24:21:"RETURN@@ TO CONTINUE":P:9N:"@@":255:}16368,0:255:24:9:"@HP@@RESS@@ RETURN @@TO CONTINUE":5020(16384)194Ĺ16368,0:5050(16384)141Ĺ16368,0:5020B5070,100,200,400,500,700,800ZN:12:::::255:M255:16368,0:24:23:"@@RETURN @@TO CONTINUE":P^ZK%664003dB100,100,200,300,650,1000,130022:1:"@HT@@RY ANOTHER?":16368,0:A$:A$"Y"A$"N"ĺ"@$":4500%"@%":A$"N"įX147:Y178:E20,1T WILL START";CR$;z"OVER. @HO@LTHERWISE, YOU CAN PRESS @HB@L TO";CR$;"GO BACK TO THE SUMMARY, OR @HRETURN@L TO";CR$;18);"STOP."16368,0:P:ZK%13ZK%27ZK%66900ZK%27ė:::(13);(4)"RUN HELLO (DON'T TOUCH)"ZK%66100 CORNER AXIS8?*N5:151,84277,84277,176151,176151,84h?4N2:162,128272,128:210,88210,172: AXES?9N2:I1622728:I,127I,129:I:I881728:208,I212,I:I: TICK MARKS?>NX155:Y124:2)14020&>6X1H712:X2H74:14030=>6X1H713:X2H73x>6Y1V811:Y2V83:5:X1,Y1X2,Y1X2,Y2X1,Y2X1,Y1:>:HC0Ē7:15010>:HC>:V115020>:IX1X2:I,Y1:N15:N:I:15030>:IY1Y2:X1,I:NI5:N:I>:V0:HC0: ? N 273,88:210,5210,167:2:32:"@@Y":X141:Y85:"X": DRAW AXES Z=."@P": PROP.SPC.=/ZY8827:208,ZY213,ZY:ZY:ZY881677:208,ZY213,ZY:ZY=/7:ZX2102778:ZX,86ZX,89:ZX:ZX2101478:ZX,86ZX,89:ZX=/>6HCH7:HC2(HC 0 H>               0         ? || !!!!!    CH  ,> "8  @     ?     n&n;ȱn/ȱ%$xo n0 ȱ0ȱxpȱo-%ox= noȥo`  w x`oLn.@& $< >,.?: ; ` 8`1UMMARY.SETABLEwwwwI  mLml n nLl m=Ll mLml m n x m&Lml= mLl mJ  mLml n mLm n mLem m m& nLrlLl x m&Lml= mLml[A0 ``x$= no nd0)ȱ0ȱ0(R0杩HphphoDh )phh elLIlphh8pȩXoDОƝCqȑop`& n nX&`Lml n m& n= m `` HAheh8& &i``枩x m n m mI0) LjLZj-h-hB!&,h0)? ,h)&,h&A-h0  JJ-h&',h0%% 0杹,h&& 'yNh'Х&&C ppp`'pLalppppp 4fnEoDmD,h07H)?!0еH el@hphh@LiL$i nLalLkC&,h(g@e@&'&ȱȱJI&@'0:,h3 ,Nh%0 Nh,h& @,hNhhLj'0",h  0 0,h&,h' nLiLj<>ŝ ढ़pLalȹo msLhixpn ȹo >гclIwBmГAe@8+h *hЪ0CCȥȄ@ nLi nȐLh!h `mIBAC@n(gklȥȑhhh hLf &ȑȑ`湥ff,` e` 4fEo` e o8EopEȥoȥp`Z jfHȱȱh`څijkl+уȥуiLvfi愠`H HHHm8knl   mimnki` f :d0V 80H    e e he f: 0Ő f : ,hhL` ` b f a f a%%:! ,Ƙ  jf ȱL]e jfȄ ᥠ L`eZ jf) I hfȱ`pZS jf68 ȱ pȱnpnpnpnp𘪠`)7`ɀ8` E` a{I mLd`I ɀ "ɎLdɏɆLdɇɐЍ >p)pp eFL` e e e e e es f mxL`: D eC, eD,L` yqqHHH$H%HDC q qLc yh%h$hhhL` e΄Ϣ($,L` e % c둃L` c%Lc hfȱ08``[A0{a0o VfEq, ppLgb d pdpEEEqiE hHH eh ehi ep eppp p fL` hf Ky hfȱii f eڢn f e eZT jfp0ɯ fLU`pppp fpp0 f:T" d fLb"< pdo, f%"!H mv f nf%Eȱȱ pd oLTaEL7a:`&<~:~:~mxq111182COPYRIGHT 1982 COMPUTER TEACHING CORP.J``LM`ƹƸ | f maL aeLKcoLai dLbm }L`r@k {Lcp d {LbtxLcyLcsLcuLcn exL'cd d {_ ` `l `` : f`               CING7p7:6:"Y = AX@U/ + BX + C , A ";(24);" 0 ."qu5:29,42211,42211,6229,6229,42: DRAW ORANGE BOXxzP2:150,68278,68278,182150,182150,68: DRAW BLUE BOX3:163,124207,124:221,124273,124:213,72213,117:213,129213,168:4:"@@YZ@@ABQ"5*(15);"S":19:33:"@@PARABOLA@@"M47:217,142198,128W>5000RN:LO%(24588)256(24589):B5:255:"@P":#####150\2:2:"A PARABOLA @@IS DESCRIBED BY AN EQUATION"f4:5:"OF THE FIRST FORM,"k"@0": STANDARD SPAALLEL TO A SIDE."255)(15);"F"@9:24:"@@ AB"W10:24:" CDEF"n11:24:" G H"12:24:" IJ KL"13:24:" MN @@GH"14:24:"@@ P @@IJK" 15:24:"@@ST @@L N"16:24:"@@W @@OPMR" 17:22:4:" IJ KL"'13:4:" MN O"?14:4:" P QR"X15:4:"ST UV"q16:4:"W X"17:4:"YZ@@ABCCDEF"(15);"S":19:7:"@@CONE@@":(15);"F"(15);"S": STANDARD FONT"@P"P4:11:"IS CUT PAR5DN:255:B4:LO%(24588)256(24589):######150?I"@P"qN2:2:"A PARABOLA @@IS FORMED WHEN A SINGLE"X4:4:"CONE..."Z(15);"S"[255\6000](15);"F"b9:4:"@@ AB"l10:4:" CDEF"v11:4:" G H"1@@C @@DESCRIBES ALL OTHERS."R5:9,9899,9899,1189,1189,98: DRAW 2ND BOXYP&17:2:"@@V@@ARIATIONS IN THESE EQUATIONS WILL MAKE"::"IT POSSIBLE TO PREDICT EXACTLY WHICH"::"TYPE OF CONIC SECTION IT REPRESENTS.":5000: PRESS RETURN:"T@@WO BASIC FORMS OF QUADRATIC EQUATIONS"V4:8:"DESCRIBE @@CONIC SECTIONS@@:"8:3:"Y = AX@U/ + BX + C DESCRIBES A @@PARABOLA,"5:9,50117,50117,709,709,50: DRAW 1ST BOX 11:16:"@@AND@@"14:3:"A@@X@U/ + @@B@@Y@U/ = ). POINT":"9). NULL SET" P9"@P": PROP.SPACING17:2:"F@@OR THOSE CONIC SECTIONS WHICH HAVE A"::"CENTER, AS DO CIRCLES, ELLIPSES, ETC.,"::"THE CENTER IS AT THE ORIGIN."5000: PRESS RETURNN:B3:"@P":255:#####150,2:3ACINGB|5:45,28229,28229,11645,11645,28: DRAW ORANGE BOX5:9:"@@1). PARABOLA":"2). CIRCLE":"3). ELLIPSE":"4). HYPERBOLA":"5). TWO LINES THROUGH"10:15:"ORIGIN"11:9:"6). TWO PARALLEL LINES":"7). TWO COINCIDENT LINES":"82:"@@S@@UCH A PLANE AND CONE CAN INTERSECT IN"e E20:2:"NINE WAYS TO FORM NINE TYPES OF @@CONIC"} J22:2:"SECTIONS." O"@@" T5000 ^N:B2:255: ####150 h"@P": PROP.SPACING r2:9:"@@@@T@@HESE NINE TYPES ARE:"w"@0": REG.SP RESET FONTm V1091:13000:18:V:" AB":13000:V1:18:" CDEF":13000:V2:18:" !#$% ":ZS.25:D V9ĢV:17:E6,3 V ,(15)"S":11:28:"@@CONIC":12:27:"SECTION" 1"@P": PROP.SPACING 67:182,88151,98 :P/ @18:N":15:18:"OPQQRS" 255c XX7331:V12:V:XX:XX20Ģ13:19:"HIJK";:19:"9";:22:"0"q 8500:XX 13:19:"HIJK";:19:"9";:22:"0" 11:18:E6,3: ERASE TOP PART OF CONE 1:1:(15)"F" 13:18:"GVIJWL" 13000:CHANGE BACK TO 200/ 1:13:"CONIC SECTIONS"e 3:2:"A@@ CONIC SECTION IS A CURVE FORMED WHEN" 5:2:"A CONE IS CUT BY A PLANE." 255:ZS2:D: PAUSE (15)"F":"@@" 11:18:" AB":12:18:" CDEF":13:18:"G9 0L":14:18:"M A"(LO%100)8 $D$"BLOAD OPENING CONE.SET, A"(LO%1128)k %D$"BLOAD PARABOLA CONE.SET, A"(LO%11281028) &(36860)170Ĺ36860,0:1750 dN:LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H nB1 x255:"@P": 1 PART ONE (1) :1(36860)17031>36860,0\(13);(4)"BRUN ENBASIC"|(24588)256(24589)3184 D$(13)(4)!LO%(24588)256(24589):(36860)17037"D$"BLOAD Z.KEY TABLE, A"(LO%) #D$"BLOAD Z.DISPLAY TABLE,                161,135Il18:25:"= 2 .":5:179,132193,132193,147179,147179,132Sv5000|N:255:B4:"@P": SETTINGS#######1:2:"W@@HAT IS THE RADIUS OF THE CIRCLE"::"EXPRESSED BY THIS EQUATION?"5:12:"3X@U/ + 3Y@U/ = 27"ZL%23:." !P1&7:91,97145,97:Y100:X113:"4"W)164,97178,97:Y100:X169:"4"^*P}+16:16:"X@U/ + Y@U/ = 4"0PN8:17:"@@T@@HEN TAKE THE SQUARE":10:2:"ROOT OF @@C@@."XPb18:14:"@@R@@ADIUS = ";(124);"4":7:150,135WHEN @@A@@ AND @@B@@"::"@0ARE BOTH EQUAL TO 1 .@P";:5:135,21147,21147,34135,34135,21dP4:24:"@@I@@F THEY AREN'T, AS":6:2:"IN THIS EQUATION..."12:14:"4X@U/ + 4Y@U/ = 16"6:19:"THEN SIMPLIFY IT SO":8:2:"THAT THEY ARE.RT.=19:7:"25 = 5, WE CAN":21:1:"SAY THAT ";(124);g3:65,16065,15886,158: SQR. RT.21:12:"@@C@@ IS THE":23:1:"RADIUS OF THE CIRCLE."4000N:255:"@P": SETTINGS####### ]2:2:"H@@OWEVER, THIS IS ONLY TRUE I,133:I-X153:Y128:"X":12:32:"Y"x13:1:"@@G@@RAPHING IT GIVES A"::"CIRCLE WITH A RADIUS"::"OF 5."H%45:A%1:B%1:C%25:K.25:1100017:7:"@@S@@INCE @@C@@ = 25":19:1:"AND ";(124);3:37,14437,14056,140: SQR8165,68: LINE FOR SQR. RT.5m10:17:"25 - X@U/"Fr10:25:"."MwP|5:149,84277,84277,182149,182149,84: ORANGE BOX6:159,132273,132:210,88210,178: DRAW AXES 6:I901757:208,I212,I:I 6:I1622738:I,13156):L(LO%1128)256H:24582,L:24583,H: SETTINGS ####### r62:5:"I@@F WE SOLVE THIS CIRCULAR EQUATION"@4:2:"FOR Y..."J6:12:"@0X@U/ + Y@U/ = 25@P"OPT8:2:"WE GET"^10:11:"@0Y = ";(95);(124)h1:107,72107,614:18:"@@C@@IRCLE":5:155,108181,108: POINTER <P"18:2:"@@O@@NLY CIRCLES WITH THEIR CENTER AT THE ORI-"::"GIN CAN BE DESCRIBED BY @@A@@X@U/ + @@B@@Y@U/ = @@C@@."'5000@,N:255:B3:"@P":LO%(24588)256(24589):H((LO%1128)214:8:"M N":15:8:"OPQQRS@@@S": DRAW CONE ;P^8:12:"IS CUT HORIZONTALLY."10:26:"@@@F AB":11:26:" CDEF":12:26:" !#$%": TOP HALF OF CONE14:26:"GVIJWL":15:26:"M N":16:26:"OPQQRS@@@S": BOTTOM HALF 5 @@AND@@ C@@ ALL HAVE"::"THE SAME SIGN, THE EQUATION DESCRIBES A"::"@@CIRCLE."u 10:14:"@@3X@U/ + 3Y@U/ = 9"| P 6:9:"@@A@@ CIRCLE IS FORMED WHEN A SIN-" 8:2:"GLE CONE...."411:8:"@@@F AB":12:8:" CDEF":13:8:"G9 0L":ILL HAVE THAT CENTER AT THE"3 21:14:"ORIGIN."L 5000: PRESS RETURN N:255:B2:"@P":LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H: SETTINGS ####### R 2:2:"I@@F @@A @@EQUALS @@B, @@AND @@A, B,35: DRAW BOX PQ 9:2:"@@V@@ARIATIONS ON THE VALUES OF @@A, B, @@AND" 11:2:"@@C @@DETERMINE WHAT THE GRAPH LOOKS LIKE." P 15:2:"@@H@@OWEVER, REGARDLESS OF THEIR VALUES,"::"ALL OF THE CONIC SECTIONS WHICH HAVE"::"CENTERS W255:"@P": SETTINGS #########] n1:1:"A@@LL OTHER CONIC SECTIONS WITH THEIR CEN-";(3); x"TERS AT THE ORIGIN ARE DESCRIBED BY EQUA-";(3);15);"TIONS OF THE FORM" 6:13:"@@A@@X@U/ + @@B@@Y@U/ = @@C@@ ." 5:79,35169,35169,5179,5179,)7 (36860)0ĺD$"BLOAD Z.DISPLAY TABLE,A"(LO%100)d #D$"BLOAD OPENING CONE.SET, A"(LO%1128) (D$"BLOAD ELLIPSE CONE.SET, A"(LO%11281028) -H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H .(36860)170Ĺ36860,0:1700 dN:B1:3 SECOND PART (2),(36860)17010H(36860)180Ĺ36860,0r(36860)0ĺ(13);(4)"BRUN ENBASIC" (24588)256(24589)3184LO%(24588)256(24589)D$(13)(4):(36860)17035 (36860)0ĺD$"BLOAD Z.KEY TABLE,A"(LO%                          UES BETWEEN 5 AND -5 FOR"::"@@A @@AND @@B@@; AND BETWEEN 64 AND -64 FOR @@C@@."~\15:14:"@@A@@X@U/ + @@B@@Y@U/ = @@C@@"f17:2:"@@V@@ALUE OF@@ A ?"p17:13:R:IzT$ZA$:5500T6ĺ"@$":17:13:(T$)2):T0:880A%T%+A% N:B3:255:9999:"@P":X(0)*2:2:"I@@F YOU WANT TO GRAPH SOME OF YOUR OWN"::"ELLIPTIC EQUATIONS, PRESS @@RETURN@@."46:2:"@@O@@THERWISE, PRESS @@ESC@@ TO CONTINUE ON.">P:ZK%13850HZK%271400M830QR10:2:"@HU@@SE VAL8:13:"= ";:N%2:NY2:9990S18:16:"32":X109:Y146:"2":7:104,144119,14418:19:"=";:N%2:NY1:9990:18:21:"16 = 4. T@@HE HORIZ-"21:2:"ONTAL RADIUS WILL THEREFORE BE 4":H34:V21:14000:21:36:"."5000: PRESS RETURN 16:10:I: INPUT** .A"4":T$ZA$:5500]T6ĺ"@$":16:10:(T$)2):T0:R:655jZA%70018:2:"W@@RONG.":71018:2:"R@@IGHT."18:9:"@@@@";:N%1:NY2:9990X64:Y136:"@@C":X64:Y146:"A":7:63,14572,145156:Y64:"32":X59:Y73:"8":7:56,7270,72mb9:12:"= ";:N%1:NY1:9990:9:15:"4 = 2. @@S@@O 2";lV9:H29:14000v9:32:"WILL"11:2:"BE THE VERTICAL RADIUS."R14:2:"@@W@@HAT WILL BE THE HORIZONTAL"::"RADIUS?"$ZA$:55009&T6ĺ"@$":3:16:(T$)2):T0:R:530F0ZA%580a:7:2:"W@@RONG.":590wD7:2:"R@@IGHT."N7:9:"@@T@@AKING THE SQUARE ROOT OF";:X245:Y43:"@@C":X245:Y55:"B@@":243,52254,52,X9:2:"@0GIVES ";:N%2:NY2:9990:XE Y-AXIS RADIUS."FX210:X1X:Y128:Y1113:9985: FLASH** VERTICALP4000sN:B2:"@P":9999:255:X(0)1:2:"W@@HAT WILL BE THE VERTICAL RADIUS OF"::"THIS ELLIPSE?"5:12:"@02X@U/ + 8Y@U/ = 32@P"3:16:I: INPUT A"2":T,115137,115137,1703,1703,115: BOX 2X(0)?P:998012:1:"N@@OTICE THAT THE X"::"COEFFICIENT DETER-"::"MINES THE RADIUS ON"::"THE X-AXIS..."X210:X1235:Y128:Y1Y:9985: FLASH**20:1:"@@A@@ND THE Y DETERMINES"::"TH"@@@@";:N%1:NY2:9990:X15:Y131:"@@A":X15:Y121:"C":7:14,13021,130: LINE & SQRTr17:5:"= @@HORIZ. RADIUS"|X15:Y145:"@@C":X15:Y156:"B":14,15421,154:19:2:"@@@@";:N%1:NY2:999020:5:"=@@ VERT. RADIUS@@"'5:3ONLY BE"::"TRUE WHEN @@A @U. B = C."::"I@@T WORKS IN THIS CASE"^ @18:1:"ONLY BECAUSE"z J20:8:"9 @U. 4 = 36." TP:9980: ERASE ^10:1:"@PA@@ RULE WHICH WORKS FOR"::"@@ALL@@ ELLIPTICAL EQUA-"::"TIONS OF THIS TYPE IS:@0"`h16:2:E@@ MIGHT @@SAY THAT"X 14:1:"@@";:N%1:NY1:9990:14:2:"A @@DEFINES THE VERTI-" 16:1:"CAL RADIUS, AND ";:N%1:NY1:9990:16:17:"@@B@@" "18:1:"DEFINES THE HORI-"::"ZONTAL RADIUS. @@BUT@@..." ,P:9980C 612:1:"T@@HIS WOULD 4 AND @@B = 9,"K 14:1:"@@AND ";:N%1:NY1:9990:14:6:"4 = 2...."o X210:Y128:X1210:Y1113:9985 18:2:"AND ";:N%1:NY1:9990:18:7:"9 = 3..." X210:X1235:Y128:Y1Y:9985 4000: RETURN 9980: ERASE 12:1:"@PW@@@U/ + 9Y@U/ = 36"+ 2:25:"@PWE GET AN" 4:3:"ELLIPSE WITH A VERTICAL RADIUS OF 2,"::"AND A HORIZONTAL RADIUS OF 3." 20000: DRAW BOX & AXES A%4:B%7:C%36:H%40:K.25:11000 4000 24:20:E20 12:1:"@P@HS@LINCE @@A@@ =6860)0ĺD$"BLOAD Z.DISPLAY TABLE,A"(LO%100)D (36860)1701900s #D$"BLOAD HYPERBOLA CONE.SET, A"(LO%1128) (D$"BLOAD SECOND HYPER.SET,A"(LO%11281028) dN:B1:9999:"@P":255:X(0) n2:3:"G@@RAPHING THIS EQUATION," x8:11:"@04X6 PART THREE (3)+(36860)17010@(36860)18010M36860,0w(36860)0ĺ(13);(4)"BRUN ENBASIC" (24588)256(24589)3184LO%(24588)256(24589)D$(13)(4):(36860)0ĺD$"BLOAD Z.KEY TABLE,A"(LO%)- :(3                            SE VALUES BETWEEN 5 AND -5 FOR @HA @LAND";CR$;"@HB@L, AND BETWEEN 64 AND -64 FOR @HC@L."14:12:"@HA@LX@U/ + @HB@LY@U/ = @HC@L"16:2:"@HV@LALUE OF @HA ?";16:14:R:IT$ZA$:5500T6ĺ"@$":16:15:(T$)2):T0:670A%T%XN:B3:7000: SETTINGSb2:2:"@HI@LF YOU'D LIKE TO GRAPH YOUR OWN";CR$;"HYPERBOLIC EQUATIONS, PRESS @HRETURN@L.";CR$;"@HO@LTHERWISE, PRESS @HESC@L TO CONTINUE."lP:ZK%13ZK%27ZK%66620qZK%66300vZK%271000X9:2:"@HU@LY140:"1":Y149:X191:"2":187,148197,148:19:30:"X ."N22:2:"@HS@LO THE EQUATION IS Y = ";(95);:X174:Y164:"1":X173:Y174:"2":172,172181,172S22:27:"X ."U2:130,160198,160198,182130,182130,160V5000: PRESS RETURN49,148r019:9:"@LX = ";(95);" ";:Y140:N%1:NY2:9990:X103:Y140:"4":X100:Y149:"16":7:99,148107,148519:17:"X":19:18:"= ";(95);:X144:Y140:"2":X144:Y150:"4":143,148151,148?19:23:"X":D19:25:"= ";(95):X191:16:2:"@HW@LRONG."[16:8:"@HT@LO DERIVE IT, USE Y =";(95);:N%1:NY2:Y116:9990X200:Y116:"@HA":X200:Y127:"B@L":7:199,125205,12516:32:"X :"&19:3:"Y=";(95);:Y140:9990:Y140:X44:"@HA":Y149:X44:"B@L":7:43,1482:156,77212,77212,112156,112156,77:12:24:"Y=";(95):X186:Y82:"1":X186:Y92:"2":7:183,89191,89:12:29:"X"9:34:(126)P:"@P"ZK%64ZK%68Ģ9:36:"@H";(ZK%):500470(ZK%)"C"Ģ16:2:"@HR@LIGHT.":520ION OF THE ASYMPTOTES?"99:6:"@HA";9);"B";10);"C"2:18,7754,7754,11118,11118,77:12:X24:"@LY=2X": 1ST QUES 2:84,77134,77134,11284,11284,77:12:14:"Y= X":X109:Y80:"1":X109:Y91:"2":7:107,89115,89: 2ND QUES }@HW@LRONG."<|12:8:"@HT@LHE POSITIVE VARIABLE, IN THIS"14:4:"CASE Y , DETERMINES THE AXIS THE";CR$;"HYPERBOLA LIES ON; HENCE IT'S THE";CR$;"Y-AXIS."5000: PRESS RETURN6:1:E40,20: ERASE7:1:"W@LHAT IS THE EQUATTION,"+65:11:"@0-4X@U/ + 16Y@U/ = 64"u@8:2:"@HW@LHICH AXIS WOULD YOU SAY IT LIES ON";CR$;5);"(X OR Y) ?"J10:19:(126);"@P"OP:"@P"TZK%89ZK%88Ģ10:21:(ZK%):360^335hZK%89Ģ12:2:"@HR@LIGHT.":380 r12:2:" SEE";CA$;"WHICH VARIABLE IN THE EQUATION (X OR Y)";CA$;"HAS THE POSITIVE COEFFICIENT. @@T@@HAT'S THE";CA$;"AXIS IT'S ON." 5000: PRESS RETURN ,N:B2:CA$(3):CR$(13)(13):9999:"@S@P":255: SETTINGS #######12:2:"L@@OOKING AT THIS EQUAND BOXK 3:214,40214,116:162,76263,76:Y30:X210:"Y": SECOND AXESv 8:29:"@F@LPQRST":12:29:"UVWXY@S" 3:195,95168,114:195,56168,36 231,95258,114:231,56258,36 6000z 17:2:"@S@HT@LO FIND WHICH AXIS IT LIES ON, JUST SIDE T 7:13:"@L I";(3);"JK";(3);"L";(3);"MN";(3);" O": RIGHT SIDE 53,5436,30:53,8136,105: EXTEND LEFT SIDE 93,54113,30:93,81113,105 6000 3:25:"@SOR LIKE THIS:" 5:155,27271,27271,120155,120155,27: 2 SETTINGS ####G n1:1:"A @LHYPERBOLA MAY LOOK";CA$;4);"LIKE THIS,"| x5:3,27141,27141,1103,1103,27: FIRST BOX 3:7,68130,68:73,3273,106:9:20:"@LX": FIRST AXES 7:8:"@F@HT";(3);"UV";(3);" W";(3);"XY";(3);"Z": LEFT860)0ĺD$"BLOAD Z.DISPLAY TABLE, A"(LO%100)B "(36860)18037p #D$"BLOAD HYPERBOLA CONE.SET,A"(LO%1128) $D$"BLOAD SECOND HYPER.SET,A"(LO%2156) %9999 &(36860)170Ĺ36860,0:1600 dN:B1:CA$(3):CR$(13)(13):9999:"@S@P":255:1 FOURTH PART (4),(36860)17010A(36860)18010N36860,0x(36860)0ĺ(13);(4)"BRUN ENBASIC" (24588)256(24589)3184LO%(24588)256(24589)D$(13)(4)(36860)0ĺD$"BLOAD Z.KEY TABLE,A"(LO%)- (36                      SOLVE THIS ONE";CR$;"FOR X..."(/"@0"C47:16:"4X@U/ =16..."J>PH10:17:"X@U/ = ";:Y67:"16":X152:Y77:"4":3:150,75158,75:10:24:"..."MPR12:17:"X@U/ = 4..."WP\15:17:"X = ";(95);:N%1:NY1:9990:15:X157:"42" P^15:2:"...@HB@LECAUSE BOTH REMAINING TERMS MUST";CR$;4);"HAVE THE SAME SIGN."h5000y N:B4:7000*1:1:"T@LAKING SUCH AN EQUATION AND SOLVING FOR";CR$;"THE VARIABLE REVEALS WHY TWO PARALLEL";CR$;"LINES ARE PRODUCED. @HI@LF WE SSING, BECAUSE AS MEN-";CR$;"TIONED ABOVE, EITHER @HA@L OR @HB@L IS ZERO."T5000[N2:2:"T@LHIS EQUATION WILL FORM TWO PARALLEL";CR$;"LINES..."5:14:"3X@U/ = 52"P 9:2:"@HB@LUT THIS ONE WON'T...";CR$;(13);11);"-3X@U/ = 5N WILL LOOK LIKE"c10:2:"ANY OF THESE:";CR$;5);"2Y@U/ = 52";6);"X@U/ = 16";6);"4Y@U/ = 64"2:16,81252,81252,9916,9916,81:100,81100,99:174,81174,99PJ14:1:"@HO@LNE OF THE VARIABLES - EITHER X OR Y -";CR$;"IS, OF COURSE, MI BOX(22:10:"GIVES THE TWO LINES."25000CN:B3:70002:2:"W@LHEN EITHER @HA@L OR @HB@L IS EQUAL TO ZERO, AND";CR$;"THE REMAINING TWO TERMS HAVE THE SAME";CR$;"SIGN, @HTWO DISTINCT PARALLEL LINES@L ARE";CR$;"FORMED. @HS@LUCH AN EQUATIO878,148l19:13:"X"Fv2:28,136104,136104,16328,16328,136y19:17:"AND Y = - ";:Y140:9990: SQR. RT.Y140:X198:"@HA":X198:Y150:"B@L":3:196,148205,14819:31:"X"2:140,136224,136224,163140,163140,136: FIFTH105,83105,67: 3RD BOXtD12:1:"YOU CAN EXPECT TO GRAPH @HTWO STRAIGHT";CR$;7);"@HLINES THROUGH THE ORIGIN@L."N16:9:"@HG@LRAPHING THE EQUATIONS"X19:6:"Y = ";:Y140:NY2:N%1:9990: SQRTbX72:Y140:"@HA":Y150:X72:"B@L":3:70,14+4:13:"@HA@LX@U/ + @HB@LY@U/ = @HC@L"`5:77,16179,16179,3777,3777,16: 1 ST BOX 7:1:"WHEN @HA , B@L HAVE OPPOSITE SIGNS"&5:35,42221,42221,6135,6135,42: 2ND BOX 010:9:"AND @HC@L = 0":105,67151,67151,83LOTICE THAT THE LINES";CA$;"INTERSECT AT THE ORI-";CA$;"GIN, AS THEY ALWAYS";CA$;"WILL REGARDLESS OF";CA$;"THE VALUES YOU CHOOSE";CA$;"FOR @HA@L AND @HB@L."4500A$"Y"100N:B2:7000"@0"1:4:"S@LO IN ANY EQUATION OF THE FORM":230 R: 20:2:"@HC@L IS UNDERSTOOD TO BE ZERO."C C%0y "23:2:"@HP@LRESS @HRETURN@L TO SEE YOUR GRAPH." ,P:ZK%13320 6300 @N:12000 J9500 T BAD VALS K.25:H%1:110001:1:"@HH@LERE'S YOUR GRAPH.";CA$;"@HN@$:55003 T6ĺ"@$":18:33:(T$)2):T0:230O K$"POSITIVE"T%0257k K$"NEGATIVE"T%0257t 260 21:2:"@$";K$;" @HNUMBERS ONLY!":ZS2:D:21:2:25):18:33:(T$)2):230 B%T% B%0B%5B%5ĺ"@$":18:33:(T$)2):R:I T$ZA$:5500C T6ĺ"@$":16:15:(T$)2):T0:170M A%T% A%5A%5A%0ĺ"@$":16:15:(T$)2):170 (A%)1K$"POSITIVE":225 K$"NEGATIVE" 18:2:"@HE@LNTER A ";K$;" VALUE FOR @HB@L" 18:33:R:I T$ZA%13ZK%27ZK%66120* }ZK%665070: ZK%27500 9:2:"@HU@LSE VALUES BETWEEN 5 AND -5 FOR @HA @LAND";CR$;"@HB@L, AND BETWEEN 64 AND -64 FOR @HC@L." 14:12:"@HA@LX@U/ + @HB@LY@U/ = @HC@L" 16:2:"@HV@LALUE OF @HA ? "; 16:140)0ĺD$"BLOAD Z.DISPLAY TABLE,A"(LO%100)4 %9998K ((36860)1702100\ dN:B1:7000 n2:2:"I@LF YOU'D LIKE TO MAKE UP YOUR OWN EQUATIONS";CR$;"AND SEE THEM GRAPHED, PRESS @HRETURN@L.";CR$;"@HO@LTHERWISE, PRESS @HESC@L TO CONTINUE." xP:ZK7 PART FIVE (5)*(36860)17010?(36860)18010L36860,0v(36860)0ĺ(13);(4)"BRUN ENBASIC" (24588)256(24589)2156LO%(24588)256(24589)D$(13)(4)(36860)0ĺD$"BLOAD Z.KEY TABLE,A"(LO%)* (3686                7,178167,96,\22:27:"X@U/ + Y@U/ = -4"Tf2:220,99220,162:171,132266,132mk5000: PRESS RETURNpN:"@P":2:1:"@HY@LOU'VE REACHED THE END OF @HCONICS@L.";CR$;"@HI@LF YOU WISH TO REVIEW ANY PART OF THE";CR$;"PROGRAM, PRESS @HESC@L, AND I27,9627,40:2:78,4378,93:33,68123,68W>3:77,6779,6779,6977,6977,67: POINTaC6500H14:1:"...AND, FINALLY, THE";CR$;"@HNULL SET@L WHEN @HA,B @LHAVE";CR$;"THE SAME SIGN BUT @HC@L HAS";CR$;"THE OPPOSITE." R1:167,96273,96273,1781632174,135:246,129252,132246,135<5000: PRESS RETURNX N:B6:7000: SETTINGS*2:2:"I@LF @HA@L AND @HB@L HAVE THE SAME SIGN AND";CR$;"@HC@L = 0, IT'S A @HPOINT@L AT THE ORIGIN...";CR$;CR$;30);"X@U/ + Y@U/ = 0")41:27,40127,40127,96COME CLOSER TOGETHER.";CA$;"@HF@LINALLY, WHEN @HC@L = 0,";CR$;" X@U/ = 0"1:147,88273,88273,176147,176147,88:2:210,96210,168:154,132266,13219:1:"IT'S @HTWO COINCIDENT";CA$;"PARALLEL LINES.@L"# 3:168,132252,132:174,129168,1206,76:144,51270,51D7:1:"IT'S @HTWO PARALLEL";CA$;"LINES."i3:154,39262,39:154,64262,64159,36154,39159,42:159,61154,64159,67:257,36262,39257,42:257,61262,64257,676500L12:1:"@HA@LS @HC@L DECREASES, THEY";CA$;"12266,168:175,168266,1124v5000: PRESS RETURNPN:B5:7000: SETTINGS1:1:"W@LHEN @HA@L OR @HB@L IS ZERO, AND THE ONE THAT";CA$;"ISN'T HAS THE SAME SIGN AS @HC@L...";CR$;" X@U/ = 4"1:141,24273,24273,78141,78141,24:2:206,264:1:"@HB@LUT WHEN @HC@L IS ALLOWED";CR$;"TO BE ZERO,";CR$;" 3X@U/ - 4Y@U/ = 0"X1:161,104275,104275,176161,176161,104:2:220,106220,174:164,140272,140b20:1:"THE GRAPH IS @HTWO LINES@L";CR$;"@HCROSSING AT THE ORIGIN.@L"l3:175,1TOTES."KY44:X50:"@F";(91);(13);" ";(92);(13);(93): LEFT HYPER&Y44:X83:"@F";" ";(96);(13);(95);(13);" ";(16)0"@S":3:49,4524,28:49,6624,84:97,45123,28:97,66123,84D1:28,25119,89:28,86119,25I6500RN1@L AND @HB@L HAVE OPPOSITE SIGNS, AND @HC@L IS";:3:23:"ANYTHING BUT ZERO,";CR$;" 3X@U/ - 4Y@U/ = 12"1:3,16145,16145,963,963,16:2:74,1874,92:7,56140,56: 1ST BOX & AXES7:23:"THE GRAPH IS A";CR$;"@HHYPERBOLA@L WITH TWO";CR$;"ASYMP141,96:2:206,98206,160:146,128266,128: 2ND BOX & AXES 16:1:"...THEN NEITHER ARE";CR$;"THE RADII, SO THE";CR$;"GRAPH IS AN @HELLIPSE@L." 26060:15:26:EL$ "@S" 5000: PRESS RETURN N:B4:7000: SETTINGSh1:1:"I@LF @HA0:146,48266,48: 1ST BOX & AXES Z 5:1:"@0...THE GRAPH IS A";CR$;5);"@HCIRCLE@L."t 26050:4:X178::CC$~ 6500 10:1:"@HB@LUT IF @HA@L AND @HB@L ARE";CR$;"NOT EQUAL...";CR$;" 3X@U/ + 5Y@U/ = 16"; 1:141,96275,96275,164141,16421:"@P@LDESCRIBES ALL OTHER";:22:8:"CONIC SECTIONS:"B h5000^ N:B3:7000: SETTINGS 1:1:"I@LF @HA=B @LAND @HA,B,C@L ALL HAVE THE SAME SIGN..." 3:3:"@03@LX@U/ + 3Y@U/ = 16"# 1:141,16275,16275,84141,84141,16:2:206,18206,871,7271,133& 11:13:26010:P2$: "141,72141,133R ,11:23:26020:P3$f 6205,72205,133~ @11:32:26030:P4$ E6500 J20:1:"@0@S@LAND @HA@LX@U/ + @HB@LY@U/ = @HC@L" T27,146133,146133,16427,16427,146: BOTTOM BOX8 ^20:L AND KNOW HOW TO RECOGNIZE";CA$;19);"THEM."7 6500Y 7:4:"@0Y = AX@U/ + BX + C" 1:15,40141,40141,6415,6415,40: 1ST BOX 7:22:"@PDESCRIBE @HPARABOLAS:@L" 1:3,72275,72275,1333,1333,72: MAIN BOX 26000:11:3:PR$  SIXTH PART (6)3(13);(4)"BRUN ENPACK"> 34470PD$(13)(4)ldN:B1:7000: SETTINGSn10:13:"@2@HSUMMARY@1"x5000N:B2:7000: PRESS RETURN- 1:1:"N@LOW WE'VE EXPLORED ALL OF THE TYPES OF";CA$;"@HCONIC SECTIONS@            @@@  @ 0@A>@ @ @0 >A @ @@@ @ CH 0@  @@ @@  p`xp`@` H@  @@  @@@ d`||`@?< P  0 @@``@<0 d`<  ``< P |`|@?   @@ @@   CH(13)(19)" "(20)(13)(21)" "(22)~$eEL$EL$(13)"9"(23)(24)(25)(26)(28)(29)(30)"8":UeP4$"@F @HPQRS"(13)"TUV"(13)"W"(13)"X"(13)"YZ"(31)(13)" @LABCD"Y#e#eCC$"@F @LEFGHIJ"(13)"K8 9L"(13)"M N"(13)"O P"(13)"Q' ^R"(13)" STUVWX@S":8$eEL$"@F^@LYZ"(123)(124)(125)(126)(127)"'"@F! #"(13)"$ %"(13)"&' ^("(13)" ) *"(13)" +,-./":"eP2$"@F 01234"(13)" 5 6"(13)"78 9:"(13)"; <"(13)"= >":"eP3$"@F?@HABC"(13)" DEF"(13)" G"(13)" H"(13)" IJK"(13)"LMNO":S#2:X1,I:NI5:N:I#!:V0:HC0:5! N CORNER AXISb!*N5:151,84277,84277,176151,176151,84!4N2:162,128272,128:210,88210,172: AXES!9N2:I1622728:I,127I,129:I:I881728:208,I212,I:I: TICK MARKS!>NX155:Y124:J"ePR$",86ZX,89:ZX /2 6HCH7:HC2(HC2)14020P 6X1H712:X2H74:14030g 6X1H713:X2H73 6Y1V811:Y2V83:5:X1,Y1X2,Y1X2,Y2X1,Y2X1,Y1: :HC0Ē7:15010 :HC :V115020 :IX1X2:I,Y1:N15:N:I:15030!:IY1Y37,177137,1: ORANGE BOX n.6:147,88273,88:210,5210,167:2:32:"@@Y":X141:Y85:"X": DRAW AXES ."@P": PROP.SPC./ZY8827:208,ZY213,ZY:ZY:ZY881677:208,ZY213,ZY:ZY /7:ZX2102778:ZX,86ZX,89:ZX:ZX2101478:ZX:P988(Y7):PX1488X63:H05 +PY1PY17511028Y+PYPYH%:P9P9H%:PX,PY:PX,P9`+Xz+J11030,11031:11035+IL3:LL4:SK:XILS:11010+IL4:LL2:S.25:11010+H%0:. SUBROUTINE FOR AXIS & BOX.5:137,1277,1277,1771 9":17:X90:"012345678@S"M*RX160:Y116:"MINOR":121,104121,135f*\5000: PRESS RETURN*fN:255:B9:"@P": SETTINGS #######*+p2:1:"A@@LL ELLIPSES FORMED BY @@A@@X@U/ + @@B@@X@U/ = @@C@@"::"ARE CENTERED ON THE ORIGIN, AND THEIR":F:*)('&%$#":Y60:X90:"= !":Y68:X90:"- 9":Y76:X90:"012345678@S")*5:90,68151,68:X160:Y60:"MAJOR")4P)>12:2:"AND THE MINOR DIAMETER IS THE WIDTH:"!*HX90:14:"@F:*)('&%$#":15:X90:"= !":16:X90:"- @S@@E@@LLIPSE":5:128,132146,132;(5000: PRESS RETURNe( N:255:B8:"@P": SETTINGS ########(2:2:"E@@VERY ELLIPSE HAS A MAJOR DIAMETER AND A"::"MINOR DIAMETER. @@T@@HE MAJOR DIAMETER IS THE"::"LENGTH OF THE ELLIPSE,"X) X90:Y52:"@20:" FG HI":13:20:" JK LM":14:20:" @@U @@UC"q'15:20:" WXY @@B":16:20:" DEFGHVW"'17:20:" @@N@@X@@PQRST":18:20:" VWXY Z@@AY":19:20:"C@@G @@DEFGHVJ":20:20:"KL MN":21:20:" OPQRRRST@@G""(17:12:"ENTERED ON THE ORIGIN. @@I@@T'S"j&8:3:"FORMED BY A CONE CUT AT AN ANGLE NOT"::"TOUCHING ITS BASE:"&LO%(24588)256(24589)&H((LO%11281028)256):L(LO%11281028)256H:24582,L:24583,H>'10:20:"@F ABC":11:20:" D E":12:175,115159,115159,135156,131: SQUARE ROOT F%16:27:"."P%5000y%N:255:B7:"@P": SETTINGS###### &2:3:"I@@F @@A, B, @@AND @@C@@ HAVE THE SAME SIGNS BUT"::"@@A ";(24);" B,@@ THE EQUATION WILL DESCRIBE AN"::"@@ELLIPSE,@@ C:: AXIS OF SYMM.`@H@@ @@@0 ``p@0p~?@8@0@  @@@@@@@@@@  @0@p~@?@80p `xp`8@` 0@` @0 `@8```p@ @0  @ 0@ @@@@ @Hp`|@8`` ?`@@@@@ ~ @ ~@@ @@  @@ @@  @@@ @@ @@@  @@ @`CH    56):L(LO%1128)256H:24582,L:24583,H: SETTINGS ####### rb2:5:"I@@F WE SOLVE THIS CIRCULAR EQUATION"l4:2:"FOR Y..."v6:12:"@0X@U/ + Y@U/ = 25@P"P8:2:"WE GET"10:11:"@0Y = ";(95);(124)1:107,72107,614:18:"@@C@@IRCLE":5:155,108181,108: POINTER <P"18:2:"@@O@@NLY CIRCLES WITH THEIR CENTER AT THE ORI-"::"GIN CAN BE DESCRIBED BY @@A@@X@U/ + @@B@@Y@U/ = @@C@@."'5000@XN:255:B3:"@P":LO%(24588)256(24589):H((LO%1128)214:8:"M N":15:8:"OPQQRS@@@S": DRAW CONE ;P^8:12:"IS CUT HORIZONTALLY."10:26:"@@@F AB":11:26:" CDEF":12:26:" !#$%": TOP HALF OF CONE14:26:"GVIJWL":15:26:"M N":16:26:"OPQQRS@@@S": BOTTOM HALF 5 @@AND@@ C@@ ALL HAVE"::"THE SAME SIGN, THE EQUATION DESCRIBES A"::"@@CIRCLE."u 10:14:"@@3X@U/ + 3Y@U/ = 9"| P 6:9:"@@A@@ CIRCLE IS FORMED WHEN A SIN-" 8:2:"GLE CONE...."411:8:"@@@F AB":12:8:" CDEF":13:8:"G9 0L":ILL HAVE THAT CENTER AT THE"3 21:14:"ORIGIN."L 5000: PRESS RETURN N:255:B2:"@P":LO%(24588)256(24589):H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H: SETTINGS ####### R 2:2:"I@@F @@A @@EQUALS @@B, @@AND @@A, B,35: DRAW BOX PQ 9:2:"@@V@@ARIATIONS ON THE VALUES OF @@A, B, @@AND" 11:2:"@@C @@DETERMINE WHAT THE GRAPH LOOKS LIKE." P 15:2:"@@H@@OWEVER, REGARDLESS OF THEIR VALUES,"::"ALL OF THE CONIC SECTIONS WHICH HAVE"::"CENTERS W255:"@P": SETTINGS #########] n1:1:"A@@LL OTHER CONIC SECTIONS WITH THEIR CEN-";(3); x"TERS AT THE ORIGIN ARE DESCRIBED BY EQUA-";(3);15);"TIONS OF THE FORM" 6:13:"@@A@@X@U/ + @@B@@Y@U/ = @@C@@ ." 5:79,35169,35169,5179,5179,)7 (36860)0ĺD$"BLOAD Z.DISPLAY TABLE,A"(LO%100)d #D$"BLOAD OPENING CONE.SET, A"(LO%1128) (D$"BLOAD ELLIPSE CONE.SET, A"(LO%11281028) -H((LO%1128)256):L(LO%1128)256H:24582,L:24583,H .(36860)170Ĺ36860,0:2240 dN:B1:3 SECOND PART (2),(36860)17010H(36860)180Ĺ36860,0r(36860)0ĺ(13);(4)"BRUN ENBASIC" (24588)256(24589)3184LO%(24588)256(24589)D$(13)(4):(36860)17035 (36860)0ĺD$"BLOAD Z.KEY TABLE,A"(LO%         ! !!!!!!!!!" """""""""Hx` @ !A@  @ @@@@  @@@@x8@`0 @  @ 0@@@@@@@@@@0@ @@ 0@ pp| @`@0`8@p|@8  @@`@8  @@` @`p @@`@`px`p  @ p`xp`@`@@ @ CH@ `px ` @@@@@@@@@@@@   P@@RESS THE & KEY IF YOU NEED A SQUARE"D 7:13:"ROOT SYMBOL."S10:17:IgA""(ZA%1Ģ12:2:"R@@IGHT!":1340212:2:"W@@RONG."A<12:9:"@@F@@IRST DIVIDE THROUGH BY 4 (THE":14:2:"VALUE OF @@A@@ AND @@B@@), MAKING @*8:9:"@@C@@IRCLES DESCRIBED BY THIS"v10:2:"FORM OF EQUATION ALWAYS HAVE THEIR"::"CENTER AT THE ORIGIN."5000N: THIRD QUESTION #####1:2:"W@@HAT IS THE RADIUS OF THIS CIRCLE?"3:12:"4X@U/ + 4Y@U/ = 40")5:2:"@@165,90151,90151,78t5000B~N: NEW SCREEN#####!!!!"#"S$!%w2:2:"W@@HERE IS THE CIRCLE'S CENTER LOCATED?"4:12:"3X@U/ + 3Y@U/ = 27"6:16:ZL%10:IA"@LORIGIN":O"0,0"ZA%1Ģ8:2:"R@@IGHT.":12208:2:"W@@RONG."29:I$A"3"5.ZA%1Ģ7:2:"@0R@@IGHT.":1090M87:2:"@0W@@RONG."B7:9:"@P@@D@@IVIDING THROUGH BY 3, 27 BECOMES"L9:2:"9 , WHOSE SQUARE ROOT IS 3 . @@S@@O THE"V11:2:"CIRCLE HAS A RADIUS OF 3 ."`j5:151,78165,78161,135I18:25:"= 2 .":5:179,132193,132193,147179,147179,132S5000|N:255:B4:"@P": SETTINGS#######1:2:"W@@HAT IS THE RADIUS OF THE CIRCLE"::"EXPRESSED BY THIS EQUATION?"5:12:"3X@U/ + 3Y@U/ = 27"ZL%23:." P17:91,97145,97:Y100:X113:"4"W164,97178,97:Y100:X169:"4"^P}16:16:"X@U/ + Y@U/ = 4"P8:17:"@@T@@HEN TAKE THE SQUARE":10:2:"ROOT OF @@C@@."P18:14:"@@R@@ADIUS = ";(124);"4":7:150,135WHEN @@A@@ AND @@B@@"::"@0ARE BOTH EQUAL TO 1 .@P";:5:135,21147,21147,34135,34135,21d\Pf4:24:"@@I@@F THEY AREN'T, AS":6:2:"IN THIS EQUATION..."p12:14:"4X@U/ + 4Y@U/ = 16"z6:19:"THEN SIMPLIFY IT SO":8:2:"THAT THEY ARE.RT.= 19:7:"25 = 5, WE CAN":21:1:"SAY THAT ";(124);g*3:65,16065,15886,158: SQR. RT.421:12:"@@C@@ IS THE":23:1:"RADIUS OF THE CIRCLE.">4000HN:255:"@P": SETTINGS####### ]R2:2:"H@@OWEVER, THIS IS ONLY TRUE I,133:I-X153:Y128:"X":12:32:"Y"x13:1:"@@G@@RAPHING IT GIVES A"::"CIRCLE WITH A RADIUS"::"OF 5."H%45:A%1:B%1:C%25:K.25:11000 17:7:"@@S@@INCE @@C@@ = 25":19:1:"AND ";(124);3:37,14437,14056,140: SQR8165,68: LINE FOR SQR. RT.510:17:"25 - X@U/"F10:25:"."MP5:149,84277,84277,182149,182149,84: ORANGE BOX6:159,132273,132:210,88210,178: DRAW AXES 6:I901757:208,I212,I:I 6:I1622738:I,131H@0xp l @x~@?p 0<@@  @@@  @@ @  @@@ @@  0@xp   @@@  @@@ h `@  @00@ @ c @@@ CH`0@0@`px` @`px `!! ! ! ! 3,60213,76127,76127,60,$l PAUSE ######$v12:2:"@P@@GRAPHS AS A @@CIRCLE@@ WITH CENTER AT THE"::"ORIGIN, WHOSE RADIUS CAN BE PREDICTED"$16:2:"BY FINDING THE VALUE OF":X165:Y117:"@@C":X165:Y128:"A@@":7:161,126173,1265%7:UATION"l#D6:13:"@0@@A@@X@U/ + @@B@@Y@U/ = @@C@@":5:77,34179,34179,5477,5477,34: EQUATION & BOX #N PUT PAUSE HERE#########X9:2:"WHEN @@A = B@@":43,6087,6087,7643,7643,60: BOX & A=B $b9:15:"AND @@A, B, C > 0":127,6021"WHICH IS THE SQUARE"::"ROOT OF":X60:Y91:"@@C":X60:Y100:"A@@":7:56,9970,99"13:12:"IN YOUR":15:1:"EQUATION.""4500: TRY ANOTHER?"&A$"Y"1440"0N:255:B6:"@P": SETTINGS #:2:2:"T@@HUS WE HAVE LEARNED THAT ANY EQP:1390)!RAD(C%A%):RAD$((RAD),4)U!RAD1RAD$((RAD),4)" UNITS,":1790s!RAD$((RAD),4)" UNIT,"!1:1:"@@T@@HIS IS A ROUGH"::"GRAPH OF YOUR EQUA-"::"TION. @@N@@OTICE THAT"::"THE CIRCLE HAS A"::"RADIUS OF ";RAD$Y"11:1:0%  ** BEGIN COMMENTS ABOUT GRAPHB (C%)(.5((A%)))1760 1:1:"@@T@@HE VALUE YOU CHOSE"::"FOR @@C@@ IS TOO SMALL TO"::"FORM A CIRCLE BIG EN-"::"OUGH TO SHOW HERE."!10:1:"@@P@@RESS @@RETURN@@ TO TRY":12:7:"AGAIN.":16368,0:(T$)0(T$)641650 h1660Jr"@$":14:31:(T$)1):T0:R:1570}|18:2:"P@@RESS @@RETURN@@ TO SEE THE GRAPH."16368,0:P:ZK%131670N: NEW SCREEN FOR GRAPHING THE EQUATION12000: DRAW AXES & BOX9500 K.2:1100*"@$":11:17:(ZA$)1):T0:R:1480O(A%)1L$" NEGATIVE ":1560cL$" POSITIVE "14:2:"T@@YPE A";L$;"VALUE FOR @@C@@ ""14:30:R:I:T$ZA$:5500,C%T%6T61650@(A%)11630JT%64T%01650T1660^+4:13:"@0A@@X@U/ + @@B@@Y@U/ = @@C@@"`7:2:"@@T@@YPE A VALUE BETWEEN 5 AND -5 FOR"9:2:"@@A@@ AND @@B@@ (@@A = B@@ IN A CIRCULAR EQUATION)"11:16:I:T$ZA$:5500A%T%:B%T%T61530A%5A%5A%015301540@F YOU WOULD LIKE TO SEE SOME OF YOUR"::"OWN CIRCULAR EQUATIONS GRAPHED, PRESS"::"@@RETURN. O@@THERWISE PRESS @@ESC@@ TO CONTINUE."16368,0:P:ZK%27ZK%13ZK%661410ZK%271840ZK%661010N:255:"@P": SETTINGS ########@C@@ BECOME 10."::"@@T@@HE SQUARE ROOT OF @@C@@ IS THE RADIUS,"eF18:2:"WHICH IN THIS CASE IS"P7:182,133164,133164,144162,141: SQR.RT.Z18:25:"10 ."d5000: PRESS RETURNnN:B255:B5:"@P": SETTINGS #######x2:2:"I@H` ` @@ 00@ 0@@@   @@@p~@?@8p~?@8@ `  ? @@@   @ @@@@ @ @0 `` 0@@  @ @@@@  PP`@@ PHDDBAA@@ @0@00 @``` @@@@@@   AABDDH`@ 8@p@8p@@ c@CH@  @0@@0"" " " "