Evolute of Ellipse/Parametric Form

Theorem
Let $E$ be an ellipse embedded in a Cartesian plane with the equation:


 * $\dfrac {x^2} {a^2} + \dfrac {y^2} {b^2} = 1$

The evolute of $E$ can be expressed using the parametric equation:
 * $\begin {cases} a x = \paren {a^2 - b^2} \cos^3 \theta \\ b y = \paren {a^2 - b^2} \sin^3 \theta \end {cases}$


 * Evolute-of-Ellipse.png