Evolute of Ellipse/Cartesian 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 $E$ is given by the Cartesian equation:
 * $\paren {a x}^{2 / 3} + \paren {b y}^{2 / 3} = \paren {a^2 - b^2}^{2 / 3}$


 * Evolute-of-Ellipse.png