key term - Minor axis

Definition

The minor axis of an ellipse is the shortest diameter, passing through its center and perpendicular to the major axis. It defines the distance between the two closest points on the ellipse.

5 Must Know Facts For Your Next Test

1. The length of the minor axis is denoted by $2b$, where $b$ is half the length of the minor axis.
2. In standard form, the equation of an ellipse with a horizontal major axis is given by $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$, where $a > b$.
3. For ellipses centered at $(h, k)$, the equation becomes $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$.
4. The endpoints of the minor axis are located at $(0, \pm b)$ for an ellipse centered at the origin.
5. The minor axis is always perpendicular to the major axis.

Review Questions

Related terms

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

Ellipse:

A conic section formed by intersecting a plane with a cone such that it forms a closed curve.

$c$ (Focal Distance): $c$ represents the distance from each focus to the center of an ellipse and satisfies $c^2 = a^2 - b^2$.