Given a parabola with parametric equations
(1)
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(2)
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the evolute is given by
(3)
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(4)
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Eliminating and gives the implicit equation
(5)
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With , this can be solved for to give
(6)
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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.