key term - Co-vertices

Definition

Co-vertices are the endpoints of the minor axis of an ellipse. They lie on the line segment perpendicular to the major axis, equidistant from the center.

5 Must Know Facts For Your Next Test

1. The distance from the center to each co-vertex is denoted by $b$ in the standard form equations of an ellipse.
2. In the equation of an ellipse $\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1$, $b$ represents the length from the center to each co-vertex when $a > b$.
3. Co-vertices help determine the orientation and shape of an ellipse.
4. If an ellipse is horizontal, co-vertices are located along a vertical line; if it is vertical, they are located along a horizontal line.
5. The coordinates of co-vertices can be found as $(h, k \pm b)$ for a horizontally oriented ellipse or $(h \pm b, k)$ for a vertically oriented ellipse.

Review Questions

Related terms

Major Axis:

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

Minor Axis:

The shortest diameter of an ellipse that passes through its center and is perpendicular to the major axis.

Focus (Foci): Points inside an ellipse such that the sum of distances from any point on the ellipse to these points is constant.