The evolute of an ellipse specified parametrically by
(1)
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(2)
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is given by the parametric equations
(3)
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(4)
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Eliminating allows this to be written
(5)
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(6)
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(7)
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(8)
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which is a stretched astroid sometimes known as the Lamé curve.
From a point inside the evolute, four normal vectors can be drawn to the ellipse, from a point on the evolute precisely, three normals can be drawn, and from a point outside, only two normal vectors can be drawn.
The arc length and area enclosed are
(9)
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(10)
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and the curvature, and tangential angle are
(11)
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(12)
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