Definition:Diameter of Ellipse

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This page is about Diameter of Ellipse. For other uses, see Diameter.

Definition

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


Also defined as

Some sources define the diameter of an ellipse $\KK$ as a chord of $\KK$ which passes through the center of $\KK$.

This is a perfectly adequate definition of a diameter of an ellipse.

However, the definition does not work so well in the context of:

a hyperbola, as it does not encompass diameters which are not chords
a parabola, which does not have a center.


Also see

  • Results about diameters of conic sections can be found here.