Major and minor axes

Definition

The major axis of an ellipse is the longest diameter, passing through its foci. The minor axis is the shortest diameter, perpendicular to the major axis at the center.

5 Must Know Facts For Your Next Test

1. The lengths of the major and minor axes are denoted by $2a$ and $2b$, respectively.
2. The major axis lies along the line that contains both foci of the ellipse.
3. When $a > b$, the ellipse is oriented horizontally, and when $b > a$, it is oriented vertically.
4. The endpoints of the major axis are called vertices, while those of the minor axis are co-vertices.
5. In standard form, an ellipse centered at $(h,k)$ with horizontal major axis has equation $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$.

Review Questions

• What are the lengths of the major and minor axes in terms of $a$ and $b$?
• How do you determine whether an ellipse is oriented horizontally or vertically?
• What are the coordinates of the vertices and co-vertices for an ellipse centered at $(h,k)$?

Related terms

Foci: Two fixed points on the interior of an ellipse used to define and construct it. The sum of distances from any point on the ellipse to each focus is constant.

Vertices: Points where the ellipse intersects its major axis. They represent the maximum width of the ellipse.

$e$ (eccentricity): \text{A measure of how much an ellipse deviates from being circular. Calculated as } e = \sqrt{1 - \frac{b^2}{a^2}}.