Step 1:

The focus of the ellipse is .

The vertices of the ellipse are ,

The -coordinate of vertices and focus are same, so the ellipse is horizontal.

Major axis is the -axis.

The standard form of ellipse is .

where is the center of the ellipse, is the length of the major axis and is the length of the minor axis.

The center is a mid point of two vertices.

The distance between center and vertex is .

The distance between center and focus is .

Step 2:

The mid point of and is center of ellipse

The center of ellipse .

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

is the distance between center and focus .

Now .

Substitute the values of , and in standard form of ellipse.

The equation of ellipse is .

Step 3:

Graph the ellipse.

Graph the equation .

Plot the center point .

Plot the focus points and .

Plot the vertex points  , .

Solution :

The equation of ellipse is .