Parabola Inverse Curve

Author

Eric W. Weisstein
April 5, 2009

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

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

©2009 Wolfram Research, Inc. except for portions noted otherwise

Inversion Center at ((Subscript[x, 0]),(Subscript[y, 0]))

InverseCurve[{a t^2,2a t},{x0,y0,k},t]

Inversion Center at Vertex

FullSimplify[InverseCurve[{a t^2,2a t},{0,0,k},t]]//Factor

GraphicsGrid[{Show[Function[i,InverseCurvePlot[{t^2,2t},{0,0,#},{t,0,10i},
PlotRange->{{-1,1.5},{-2,2}}]]/@{-1,1}]&/@{.5,1,2}},ImageSize->400]//Quiet

Inversion Center at Focus

FullSimplify[InverseCurve[{a t^2,2a t},{a,0,k},t]]

GraphicsGrid[{InverseCurvePlot[{t^2,2t},{1,0,#},{t,-2π,2π},
PlotRange->3]&/@{.5,1,2}},ImageSize->400]