Question

Find an equation of the ellipse.

Vertices: (3, 1), (3, 9)

Minor axis length: 6

Answer 1

Step 1 :

The vertices of the ellipse are .

Length of the minor axis is 6.

Since the - coordinate of vertices are same, the ellipse is vertical.

The standard form of the ellipse is .

Where is the center, .

The center is a mid point of two vertices.

The distance between center and vertex is .

is the length of the major axis and

is the length of the minor axis.

Step 2 :

The vertices of the ellipse are .

The mid point of is center of ellipse

The center of ellipse .

Length of the minor axis :  .

The distance between center and vertex is .

The length of semi minor axis is the distance between center and vertex.

Substitute the values of , , and in .

Solution :

The equation of ellipse is .