Major axis

Definition

The major axis of an ellipse is the longest diameter, passing through its center and both foci. It defines the maximum extent of the ellipse.

5 Must Know Facts For Your Next Test

1. The length of the major axis is denoted as $2a$, where $a$ is the semi-major axis.
2. The endpoints of the major axis are known as vertices of the ellipse.
3. The major axis intersects the center and both foci of the ellipse.
4. In standard form, if $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and $a > b$, then the major axis is along the x-axis.
5. The distance between a focus and a vertex on the major axis is called the linear eccentricity, denoted as $c$, where $c^2 = a^2 - b^2$.

Review Questions

• What is the length of the major axis in terms of $a$?
• Where does the major axis intersect in an ellipse?
• If given $\frac{x^2}{9} + \frac{y^2}{4} = 1$, which axis represents the major axis?

Related terms

Minor Axis: The shortest diameter of an ellipse, perpendicular to the major axis at its center.

Foci: Two fixed points on the interior of an ellipse used in its formal definition; they lie on the major axis.

Ellipse: A set of points such that for any point on it, the sum of its distances from two fixed points (foci) is constant.