Definition:Conic Section/Focus-Directrix Property/Circle

Definition

 * CircleFocusDirectrix.png

It is not possible to define the circle using the focus-directrix property.

This is because as the eccentricity $e$ tends to $0$, the distance $p$ from $P$ to $D$ tends to infinity.

Thus a circle can in a sense be considered to be a degenerate ellipse whose foci are at the same point, that is, the center of the circle.