Definition:Diameter of Central Conic
This page is about Diameter of Central Conic. For other uses, see Diameter.
Definition
Let $\KK$ be a central conic.
A diameter of $\KK$ is the locus of the midpoints of a system of parallel chords of $\KK$.
Ellipse
Let $\KK$ be an ellipse.
A diameter of $\KK$ is the locus of the midpoints of a system of parallel chords of $\KK$.
Hyperbola
Let $\KK$ be a hyperbola.
A diameter of $\KK$ is the locus of the midpoints of a system of parallel chords of $\KK$.
Also defined as
Some sources define the diameter of a central conic $\KK$ as a chord of $\KK$ which passes through the center of $\KK$.
This is a perfectly adequate definition of a diameter of an ellipse.
Indeed, in the context of a circle, this is how a diameter is routinely defined.
However, it falls short of providing a full definition of the diameter of a hyperbola.
Hence, for the general central conic, and one that is not specifically a circle, this definition is not used on $\mathsf{Pr} \infty \mathsf{fWiki}$.
Also see
- Results about diameters of conic sections can be found here.