Dandelin's Theorem/Foci

Theorem
Let $\CC$ be a double napped right circular cone with apex $O$.

Let $\PP$ be a plane which intersects $\CC$ such that:
 * $\PP$ does not pass through $O$
 * $\PP$ is not perpendicular to the axis of $\CC$.

Let $\EE$ be the conic section arising as the intersection between $\PP$ and $\CC$.

Let $\SS$ and $\SS'$ be the Dandelin spheres with respect to $\PP$.

Then:
 * $\SS$ and $\SS'$ are tangent to $\PP$ at the foci of $\EE$.

Also see

 * Definition:Dandelin Spheres