Definition:Conic Section/Center

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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.

Circle.png


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.

EllipseParts.png


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.


HyperbolaParts.png


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.