Definition:Circle/Focus

Definition

 * CircleFocusDirectrix.png

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.

Also see

 * Circle is Limit of Ellipse as Eccentricity tends to Zero