Vertices

Definition

Vertices are the points on an ellipse that lie on the major axis and are at the maximum distance from the center. They are crucial for determining the shape and size of the ellipse.

5 Must Know Facts For Your Next Test

1. The vertices are located at $(h \pm a, k)$ for a horizontally oriented ellipse centered at $(h, k)$.
2. For a vertically oriented ellipse, the vertices are at $(h, k \pm a)$.
3. $a$ represents the semi-major axis length in both orientations.
4. The distance between the vertices is $2a$, which is twice the length of the semi-major axis.
5. Vertices help define other key features of an ellipse such as foci and eccentricity.

Review Questions

• Where are the vertices located in a horizontally oriented ellipse with center $(h, k)$?
• What is the distance between two vertices of an ellipse?
• How do you determine whether an ellipse is horizontally or vertically oriented based on its vertices?

Related terms

Major Axis:

The longest diameter of an ellipse that passes through its center and both foci.

$a$ (Semi-Major Axis): $a$ represents half of the major axis length; it stretches from the center to a vertex.

$b$ (Semi-Minor Axis): $b$ represents half of the minor axis length; it stretches from the center to a point on the edge perpendicular to the major axis.