Definition:Diameter of Conic Section
This page is about Diameter of Conic Section. For other uses, see Diameter.
Definition
Let $\KK$ be a conic section.
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 $\KK$.
Parabola
Let $\KK$ be a parabola.
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 conic section $\KK$ 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, 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.
Hence, for the general conic section, 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.
Linguistic Note
There are two adjectival forms of diameter:
Diametral
Diametral means:
- located on or forming a diameter.
Diametrical
Diametrical means:
- relating to or along a diameter.
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): diameter: 2. (of a conic)
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): diameter: 2. (of a conic)