Major axis

Definition

The major axis of an ellipse is the longest diameter, passing through its two foci and the center. It represents the maximum distance across the ellipse.

5 Must Know Facts For Your Next Test

1. The length of the major axis is equal to $2a$, where $a$ is the semi-major axis.
2. The endpoints of the major axis are called vertices.
3. The center of the ellipse lies at the midpoint of the major axis.
4. The equation for an ellipse with a horizontal major axis is $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, where $(h,k)$ is the center.
5. For an ellipse with a vertical major axis, the equation changes to $\frac{(x-h)^2}{b^2} + \frac{(y-k)^2}{a^2} = 1$.

Review Questions

• What is the relationship between the length of the major axis and the semi-major axis?
• How do you determine whether an ellipse has a horizontal or vertical major axis from its equation?
• What are the names of points where the major axis intersects with the ellipse?

Related terms

Minor Axis: The shortest diameter of an ellipse, perpendicular to its major axis and passing through its center.

Foci: Two fixed points inside an ellipse used in its formal definition; each point on the ellipse has a constant total distance to these two points.

Semi-Major Axis: $a$ in an ellipse's equation, representing half of its longest diameter.