Vertices

Definition

Vertices are the points on an ellipse that lie along the major axis and are the furthest from the center. They represent the maximum distance from the center to the edge of the ellipse.

5 Must Know Facts For Your Next Test

1. The vertices of an ellipse are located at $(\pm a, 0)$ for a horizontally oriented ellipse centered at $(0, 0)$.
2. For a vertically oriented ellipse centered at $(0, 0)$, the vertices are located at $(0, \pm a)$.
3. $a$ represents the semi-major axis length in both horizontally and vertically oriented ellipses.
4. The distance between two vertices is equal to $2a$, where $a$ is the length of the semi-major axis.
5. In standard form equations of ellipses $(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1)$, $a > b$ if vertices lie on x-axis and $b > a$ if they lie on y-axis.

Review Questions

• What coordinates represent the vertices of an ellipse centered at $(0, 0)$ with a horizontal orientation?
• How do you determine whether an ellipse's vertices lie along the x-axis or y-axis?
• If an ellipse has its center at $(3, -2)$ and has a semi-major axis length of $5$, what are its vertices?

Related terms

Semi-Major Axis: The longest radius of an ellipse extending from its center to its perimeter.

Semi-Minor Axis: The shortest radius of an ellipse extending from its center to its perimeter.

Foci: Two fixed points inside an ellipse such that the sum of distances from any point on the ellipse to these foci is constant.