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Consider an ellipse $K$.

A vertex of $K$ is either one of the endpoints of the major axis of $K$.

In the above diagram, $V_1$ and $V_2$ are the vertices of $K$.

Also defined as

Some sources also classify the covertices as vertices.

That is, they define the vertices as the endpoints of both the major axis and the minor axis.

Also see

Linguistic Note

The plural of vertex is vertices.

The word vertex is Latin for peak, from which the irregular plural form.