I have question regarding the possibility of inscribing a cone in a sphere.
Essentially, I am looking for some proper definition of that. When dealing with polyhedra, the matter is simple: each of the polyhedron's vertices must lie on the sphere. However, what conditions need to be met in order for a cone to be inscribed in a sphere? When the base is circular, I understand that the apex of the cone and the edge of the base must lie on the sphere. But can an elliptical cone be inscribed in a sphere, and if yes, would that mean that just two points from the edge of the base are on that sphere?
Intuition seems to say "yes", but as I mentioned, I would be thankful for some definition.