# Definition:Conic Section/Center

## Definition

The center of a conic section is the point midway between the foci.

### Center of Circle

The circle is usually treated differently.

From Circle has Two Coincident Foci, the foci and the center are all the same point.

In the words of Euclid:

And the point is called the center of the circle.

In the above diagram, the center is the point $A$.

### Center of Ellipse

Let $K$ be an ellipse.

The center of $K$ is the point midway between the foci.

By definition of the major axis and minor axis, this is the point where the major axis and minor axis of $K$ cross.

### Center of Hyperbola

Let $K$ be a hyperbola.

The center of $K$ is the point where the major axis and minor axis of $K$ cross.

By definition of the major axis and minor axis, this is the point midway between the foci.

### Center of Parabola

The parabola has no center.

## Also see

• Results about centers of conic sections can be found here.

## Linguistic Note

The British English spelling of center is centre.

The convention on $\mathsf{Pr} \infty \mathsf{fWiki}$ is to use the American English spelling center, but it is appreciated that there may be lapses.