\begin{definition}[Definition:Dandelin Spheres]
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 parallel to a generatrix of $\CC$
:$\PP$ is not perpendicular to the axis of $\CC$.
Hence, by construction, the resulting conic section $\EE$ is either an ellipse or a hyperbola, and is not degenerate.
Let two spheres $\SS$ and $\SS'$ be constructed so that they have ring-contact with $\CC$ such that $\PP$ is tangent to both $\SS$ and $\SS'$.
Then $\SS$ and $\SS'$ are known as '''Dandelin spheres'''.
\end{definition}