Definition:Diameter of Hyperbola/Also defined as

Definition

Some sources define the diameter of a hyperbola $\KK$ as a chord of $\KK$ which passes through the center of $\KK$:

However, while it is true that such a chord is indeed a diameter of $\KK$, not all diameter of $\KK$ are chords of $\KK$.

For example:

where it can be seen that the diameter (red) of the hyperbola (blue) defined by the parallel chords is not actually itself a chord of $\KK$.

Also see

• Locus of Midpoints of Parallel Chords of Central Conic passes through Center

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

Sources

• 1933: D.M.Y. Sommerville: Analytical Conics (3rd ed.) ... (previous) ... (next): Chapter $\text {V}$. The Hyperbola: $2$.