# 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**.

(*The Elements*: Book $\text{I}$: Definition $16$)

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

## 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.