Co-vertex

Definition

The co-vertices of an ellipse are the endpoints of the minor axis. They are perpendicular to and lie at the midpoint of the major axis.

5 Must Know Facts For Your Next Test

1. The distance from the center to each co-vertex is equal to the semi-minor axis, denoted as $b$.
2. In a standard ellipse equation $(x-h)^2/a^2 + (y-k)^2/b^2 = 1$, co-vertices are located at $(h, k \pm b)$ for horizontal ellipses and $(h \pm b, k)$ for vertical ellipses.
3. Co-vertices help determine the shape and size of an ellipse by defining its minor axis.
4. The length of the segment connecting two co-vertices equals $2b$, where $b$ is half the length of the minor axis.
5. Co-vertices lie along the line that is perpendicular to the major axis at its center.

Review Questions

• Where are the co-vertices located in relation to an ellipse's axes?
• How do you find co-vertices using an ellipse's standard equation?
• What is the relationship between a semi-minor axis and co-vertices?

Related terms

Major Axis:

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

Minor Axis:

The shortest diameter of an ellipse, perpendicular to the major axis at its center.

Foci:

Two fixed points inside an ellipse used in its geometric definition; they lie along the major axis.