Center of an ellipse

Definition

The center of an ellipse is the midpoint of both the major and minor axes, serving as the point of symmetry for the ellipse. It is typically denoted by a coordinate pair $(h, k)$ in the Cartesian plane.

5 Must Know Facts For Your Next Test

1. The center of an ellipse can be found at the midpoint of its foci.
2. In standard form equations $(x - h)^2/a^2 + (y - k)^2/b^2 = 1$ or $(x - h)^2/b^2 + (y - k)^2/a^2 = 1$, the center is $(h, k)$.
3. If an ellipse is centered at the origin, its equation simplifies to $x^2/a^2 + y^2/b^2 = 1$.
4. The distances from any point on the ellipse to each focus sum to a constant value that depends on the lengths of the major and minor axes.
5. When graphing an ellipse, knowing its center helps determine its orientation and placement in the Cartesian plane.

Review Questions

• How do you find the center of an ellipse given its standard form equation?
• What role does the center play in determining an ellipse's symmetry?
• Explain how you can verify if a given point is indeed the center of an ellipse.

Related terms

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

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

Foci: Two fixed points inside an ellipse such that the sum of distances from any point on the ellipse to each focus remains constant.