\begin{definition}[Definition:Conic Section/Focus-Directrix Property/Circle]
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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.
\end{definition}