Definition:Diameter of Conic Section/Also defined as

Definition
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.

Also see

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


 * Definition:Diameter of Conic Section