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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 $\PP$.
Let $\KK$ and $\KK'$ be the planes in which the ring-contacts of $\CC$ with $\SS$ and $\SS'$ are embedded respectively.
- The intersections of $\KK$ and $\KK'$ with $\PP$ form the directrices of $\EE$.
Also known as
Dandelin's theorem is also seen referred to as Dandelin's construction.
Source of Name
This entry was named for Germinal Pierre Dandelin.