\begin{definition}[Definition:Conic Section/Intersection with Cone]
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Let $C$ be a double napped right circular cone whose base is $B$.
Let $\theta$ be half the opening angle of $C$.
That is, let $\theta$ be the angle between the axis of $C$ and a generatrix of $C$.
Let a plane $D$ intersect $C$.
Let $\phi$ be the inclination of $D$ to the axis of $C$.
Let $K$ be the set of points which forms the intersection of $C$ with $D$.
Then $K$ is a '''conic section''', whose nature depends on $\phi$.
\end{definition}