I would like to determine the elliptical cone that contains two ellipsoids such that each ellipsoid is tangent to the cone along the corresponding ellipsoid's ellipse (as conic section).
See picture below:
In particular, if I write the ellipsoids in homogeneous quadratic form, how can I solve for the elliptical cone?
It seems like I should be able to connect the fact that each ray along the elliptical cone is simultaneously tangent to both ellipsoids. Then for each ellipsoid, these tangent points define a parametric curve that is actually an ellipse from the conic section made by a plane intersecting the cone.
@amd?