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.