Supplements

Some related information in the form of mathematica worksheets:

Proof that the path described by the parametric function is indeed an ellipse: EllipseProof.nb

Proof that the path is coplanar: EllipseCoplanarProof.nb

The relation of rho and phi to the orientation and size of the ellipse: EllipseComponents.nb

Finding the vertices of the ellipse when rho and phi are known: EllipseVertices.nb

A document discussing the determination of rho and phi to generate an ellipse with particular semimajor and semiminor axes and normal: SolvingForParametricEllipse.doc