Definition:Diameter of Ellipse/Also defined as

Definition
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

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