Definition:Diameter of Central Conic

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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 $\KK$.


Locus-of-chord-midpoints-of-ellipse.png


Hyperbola

Let $\KK$ be a hyperbola.

A diameter of $\KK$ is the locus of the midpoints of a system of parallel chords of $\KK$.


Locus-of-chord-midpoints-of-hyperbola.png


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.