Minor axis

Definition

The minor axis of an ellipse is the shortest diameter that bisects the ellipse, passing through its center and perpendicular to the major axis. It is aligned with the ellipse's shortest dimension.

5 Must Know Facts For Your Next Test

1. The length of the minor axis is represented by $2b$, where $b$ is the distance from the center to a vertex along the minor axis.
2. The endpoints of the minor axis are called co-vertices.
3. In an equation of an ellipse in standard form, $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, $b$ represents half the length of the minor axis when $a > b$.
4. The minor axis is always perpendicular to the major axis.
5. In a vertical ellipse, where $\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1$, $b$ still represents half of the minor axis.

Review Questions

• What is represented by $b$ in the standard form equation of an ellipse?
• How do you determine if an ellipse’s minor axis is vertical or horizontal?
• What are co-vertices in relation to an ellipse?

Related terms

Major Axis: The longest diameter that bisects an ellipse, passing through its center and vertices.

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

$a$ (Semi-major Axis): $a$ represents half of the major axis length in an ellipse.