Circle Negative Pedal Curve

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Initialization

<<MatthWorld`Curves`

Equations

np=FullSimplify[NegativePedalCurve[{Cos[t],Sin[t]},{x,y},t]]

(0, 0)

np/.{x->0,y->0}

(1, 0)

FullSimplify[np/.{x->1,y->0}]

(x, 0)

FullSimplify[np/.y->0]

movie=Table[ParametricPlot[{{Cos[t],Sin[t]},{((x-Cos[t])/(-1+x Cos[t])),(((-1+(x^2)) Sin[t])/(-1+x Cos[t]))}},{t,0,2Pi},
PlotStyle->{Black,Red},
AspectRatio->Automatic,
Epilog->{Red,PointSize[.02],Point[{x,0}]},
PlotRange->{{-1,1},{-1,1}}1.5,
Ticks->None,
PlotLabel->TraditionalForm["\!\(\*
StyleBox[\"x\",\nFontSlant->\"Italic\"]\) ="<>ToString[PaddedForm[x,{3,2}]]]
],{x,0,1.5,.05}]

Show[GraphicsArray[Partition[Take[movie/.PointSize[x_]:>PointSize[.06],{1,Length[movie],4}],4,4,{1,1},{}]],ImageSize->450]

Animation

<<GIF`;

Export[gifs<>"circnped.gif",movie]//Timing