Category:Definitions/Dandelin Spheres

This category contains definitions related to Dandelin Spheres.
Related results can be found in Category: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.