# 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:

$\paren {a x}^{2 / 3} + \paren {b y}^{2 / 3} = \paren {a^2 - b^2}^{2 / 3}$