I72o=,dd +(I)   1Courier New1Symbol New1Courier New1Courier NewTimes New RomanTimes New Roman1Courier New1Courier New1Courier New1Courier NewXԚVXԚVXԚVXԚV?/ <```@@@?~~~~~ԱޱޱԱ޿޿ph (((Pdd{ d< p {2 ʿ{7@w$@(@$@($@(@`}J?@???@@@@@@033333??@^ߛOw?HzG???uIc@ VF@@?@ @@@ ?P;Z ?@?@?@@dddddddddddddddddddddddddddddddddddddddd 2 2??@$$$$@($@(@???????@?حܮ0܀8~x^2y = x^2QQ2???$$$0$CXc kc섗?????????0$CXc kc섗? p22t32x42|52627282Bspp^2pi/4(x,y) = (p,p^2)2???$$$0$CXc kc섗? (AYڤ@ GJ@??????;o,Y?2?2PTjWWY-4t^3.5+3t^24(x,y) = (-4t^3,.5+3t^2); -6.000000 <= t <= 6.283190-6.00000;6.283192??h!@$$$Uy@???????Īȫ̬ЭԮدܰH2LL22pU2U2xW2-4p^3+(1+4p^2)^1.5/2*cos(t).5+3p^2+(1+4p^2)^1.5/2*sin(t)_(x,y) = (-4p^3+(1+4p^2)^1.5/2*cos(t),.5+3p^2+(1+4p^2)^1.5/2*sin(t)); 0.000000 <= t <= 6.2831900.00000;6.283192???$$$ (AYڤ@ GJ@???????? (AYڤ@ GJ@XF\G`HdIhJlKpLuX p-p(1+4p^2)p^2+.5(1+4p^2)pi/4%(x,y) = (p-p(1+4p^2),p^2+.5(1+4p^2))0.xyz/N#@JXT@0$C@@@@@@@@@@@@@@@@?@@@@@@@@@@ @ @ @The Purple Curve Shows the Centers of Curvature (Evolute)l1hBbl_n@j@YGEν@Times New Roman,NRed Vector Points Along N Hat to Center of Curvature Curvaj4tr=T# @|g1ް@/@Times New RomanNThe Center of Curvature is Marked in BlackCurvature)a}c8"{H@7da?@mVq@Times New RomanOThe Oscullating Circle is Lime GreenBlackvatureute)@ɯ$+_ ?Г@(jXw|@^+Zy@Times New Romany = x^2-m(@fYeYe/(@1Courier New Q(x,y) = (p,p^2)Q0Q/.m(@fYeYe\.4C@1Courier New Qsegment (p,p^2)-->(p-p(1+4p^2),p^2+.5(1+4p^2)).m(,Aii@b&۰7a@1Courier New |R(x,y) = (-4t^3,.5+3t^2); -6.000000 <= t <= 6.283190/.m(,Aii@b&۰?='@1Courier New 4S(x,y) = (-4p^3+(1+4p^2)^1.5/2*cos(t),.5+3p^2+(1+4p^2)^1.5/2* .m(,Aii@b&۰HdX0@1Courier New S(x,y) = (p-p(1+4p^2),p^2+.5(1+4p^2))`6Q.m(,Aii@zǻ1ęi@1Courier New @@@h!@