Given a parabola with parametric equations

the evolute is given by

Eliminating and gives the implicit equation

With , this can be solved for to give

which is known as the semicubical parabola.

From a point above the evolute, three normals can be drawn to the parabola, while only one normal can be drawn to the parabola from a point below the evolute.

See also

Evolute, Parabola, Semicubical Parabola

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Cite this as:

Weisstein, Eric W. "Parabola Evolute." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/ParabolaEvolute.html

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