Curve described by a point inside an ellipse

Question

It's well known that a point inside a circle rotating on a line describes a trochoid of parametric equation: $$x=c_0\phi-c_1\sin(\phi)$$ $$y=c_2-c_3\cos(\phi)$$ in which the constant $c_0,c_1,c_2,c_3$ are depending on its position on the diameter of the circle. My question is: if we have an ellipse with axis $a$ and $b$ and a point inside the ellipse, what is the parametric equation of the curve obtained rolling the ellipse on a line? Thanks in advance.

Answer 1

If the point is at the focus of the ellipse the curve is a Roulette of Delaunay: Here is a link: http://www.mathcurve.com/courbes2d/delaunay/delaunay.shtml