Right Strophoid Inverse Curve

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Initialization

<<Mathworld`Curves`

Equation

FullSimplify[InverseCurve[{-c,t}(((t^2)-(c^2))/((t^2)+(c^2))),{x,0,k},t]]

Together[InverseCurve[{-1,t}(((t^2)-1)/((t^2)+1)),{1,0,1},t]]

Plot

Same strophoid

With[{c=1},ParametricPlot[{
{-1,t}(((t^2)-1)/((t^2)+1)),
{((-1+(t^2))/(1+(t^2))),((-1+(t^2))/(t (1+(t^2))))}
},{t,-10,10},PlotRange->{{-1,1},{-1,1}},PlotStyle->{{Thickness[.02],Red},{}}]]

With[{c=1},
InverseCurvePlot[{-c,t}(((t^2)-(c^2))/((t^2)+(c^2))),{c,0,c},{t,-10,10},PlotRange->{{-.8,2},{-2,2}},
Ticks->True,ImageSize->200]
]

With[{c=1},
InverseCurvePlot[{-c,t}(((t^2)-(c^2))/((t^2)+(c^2))),{c,0,c},{t,-10,10},PlotRange->{{-.8,2},{-2,2}},ImageSize->200]
]

With[{c=2},
InverseCurvePlot[{-c,t}(((t^2)-(c^2))/((t^2)+(c^2))),{c,0,c},{t,-10,10},PlotRange->{{-.8,2},{-2,2}},
Ticks->True,ImageSize->200]
]