Vertices: (0, 2), (4, 2); endpoints of the minor axis: (2, 3), (2, 1)

Question

Find the standard form of the equation of the ellipse with the given characteristics.

Vertices:  (0, 2), (4, 2);  endpoints of the minor axis:  (2, 3), (2, 1)

Answer 1

Step 1:

The vertices are and minor axis end points are .

The center is midway between two vertices : .

center is .

The minor axis is the distance between center and minor axis end point :

Therefore, the minor axis .

The major axis is the distance between center and vertex :

Therefore, the major axis is .

The standard form of a ellipse is .

Solution :

The ellipse equation is .