Evolute of Ellipse/Cartesian Form

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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


Proof


Sources