Parabola Evolute

Author

Eric W. Weisstein
March 16, 2008

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

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

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

Equation

Factor[Evolute[{a t^2,a t},t]]

FullSimplify[Eliminate[{x==(1/2) a (1+6 (t^2)),y==-4 a (t^3)},t]]

FullSimplify[Solve[%/.a->1,x]]

Figure

With[{a=1},
Show[GraphicsArray[{
EvolutePlot[{a t^2,a t},{t,-2,2},
DisplayFunction->Identity,
PlotRange->{{-.1,2.5},Automatic}],
EvolutePlot[{a t^2,a t},{t,-2,2,.05},4,PlotRange->{{-.1,2.5},{-2,2}},
DisplayFunction->Identity,
AspectRatio->Automatic]
}]]
]