Definition:Conic Section/Intersection with Cone/Tilting Angle
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Definition
Let $C$ be a double napped right circular cone whose base is $B$.
Let $D$ be a plane which intersects $C$.
Let $D$ be inclined at an angle $\phi$ with the axis of $C$.
Let $K$ be the conic section formed by the intersection of $C$ with $D$.
The inclination $\phi$ of the slicing plane with the axis of $C$ is known as the tilting angle of $D$ for $K$.
Also defined as
Some analyses find it more convenient to define the tilting angle as the inclination of $D$ with the horizontal.
It is necessary to specify which is meant in any dissertation which uses the concept.
Sources
- 1992: George F. Simmons: Calculus Gems ... (previous) ... (next): Chapter $\text {A}.8$: Pappus (fourth century A.D.): Appendix: The Focus-Directrix-Eccentricity Definitions of the Conic Sections