Center of an ellipse

Definition

The center of an ellipse is the midpoint of both the major and minor axes. It is the point equidistant from all vertices of the ellipse.

5 Must Know Facts For Your Next Test

1. The coordinates of the center can be found using the midpoint formula on the major or minor axis.
2. In standard form, if an ellipse is centered at $(h, k)$, its equation is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$.
3. The center divides each axis into two equal parts.
4. Both foci are symmetrically located around the center along the major axis.
5. If you translate an ellipse, its center moves accordingly.

Review Questions

• How do you determine the coordinates of the center from an ellipse's equation?
• What role does the center play in defining other properties of an ellipse?
• What happens to the center if you perform a translation on an ellipse?

Related terms

Major Axis: The longest diameter of an ellipse that passes through its center.

Minor Axis: The shortest diameter of an ellipse that passes through its center and is perpendicular to the major axis.

Foci (singular: Focus): Two fixed points inside an ellipse such that the sum of distances from any point on the ellipse to each focus is constant.