Confocal Conics

Author

Eric W. Weisstein
October 5, 2004

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/ConfocalConics.nb.

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

©2005 Wolfram Research, Inc. except for portions noted otherwise

Plot

Show[Graphics[{
Table[Circle[{-1,0},{i,Sqrt[i^2-1^2]}],{i,1.1,2,.1}],
Table[{PolarPlot[1/e(e^2-1)/(1-e Cos[θ]),{θ,-ArcTan[Sqrt[e^2-1]],ArcTan[Sqrt[e^2-1]]},Ticks->None,DisplayFunction->Identity][[1]],
PolarPlot[1/e(e^2-1)/(1-e Cos[θ]),{θ,ArcTan[Sqrt[e^2-1]],2Pi-ArcTan[Sqrt[e^2-1]]},Ticks->None,DisplayFunction->Identity][[1]]},
{e,1.02,2,.1}],
Line[{{-4,0},{4,0}}],
Line[{{-1,-2},{-1,2}}],
{PointSize[.03],Point/@{{0,0},{-2,0}}}
}],
DisplayFunction->$DisplayFunction,AspectRatio->Automatic,
PlotRange->{{-4,2},{-2,2}}]