\begin{definition}[Definition:Circle/Focus]
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As a circle cannot be specified using the focus-directrix property, the focus cannot be defined using that technique.
Consider an ellipse $K$ with eccentricity $e$.
Let $e$ tend to zero.
Then as $e$ becomes smaller, the foci of $K$ become closer together.
In the limit, the foci coincide.
Thus the focus of the circle can be understood as being its center.
\end{definition}