Cissoid of Diocles Catacaustic

Author

Eric W. Weisstein
March 16, 2008

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneCurves/CissoidofDioclesCatacaustic.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/CissoidofDioclesCatacaustic.html.

©2008 Wolfram Research, Inc. except for portions noted otherwise

Equation

cat=FullSimplify[Catacaustic[{t^2,t^3}2/(1+t^2),{x,0},t]]

q=FullSimplify[cat /.x->8]

eqn1=Simplify[Subtract@@FullSimplify[Eliminate[{x,y}==q,t]]]

eqn2=-4 (y^2)+((x^2)+(y^2))^2+ 4x((x^2)+(y^2))

Simplify[eqn1-eqn2]

eqn3=FullSimplify[Expand[(x^2+y^2-a x)^2-a^2(x^2+y^2)]]

Simplify[eqn1-eqn3 /.a->-2]

(x^2+y^2-a x)^2-a^2(x^2+y^2)/.a->-2

Plot

CatacausticPlot[{t^2,t^3}2/(1+t^2),{8,0},{t,-40,40,.2},
PlotRange->{{-5,10},{-8,8}}]