Co-vertices of an ellipse are the two points that are located at the ends of the minor axis of the ellipse. An ellipse is defined by its two axes: the major axis and the minor axis. The major axis is the longest diameter of the ellipse, while the minor axis is the shortest.
To understand co-vertices better, consider the standard form of the equation of an ellipse centered at the origin:
(x²/a²) + (y²/b²) = 1
In this equation, a represents the length of the semi-major axis (half of the major axis), and b represents the length of the semi-minor axis (half of the minor axis). The co-vertices are located at the points (0, b) and (0, -b) on the Cartesian plane.
For example, if you have an ellipse with the equation (x²/16) + (y²/9) = 1, then a = 4 and b = 3. The co-vertices would be located at (0, 3) and (0, -3).
In summary, the co-vertices are important because they help define the shape and orientation of the ellipse, contributing to its overall geometry and helping in graphing it accurately.