Step 1:

The foci of the ellipse is $\"\"$ .

The co-vertices of the ellipse is $\"\"$ .

Observe the foci x-coordinate are equal, so the ellipse is vertical.

Ellipse equation :

The standrad form of the vertical ellipse is $\"\"$ .

Where a is the length of the semi major axis, b is the length of the semi minor axis.

Here center of the ellipse is $\"\"$ .

Foci of the ellipse is $\"\"$ .

Vertices of the ellipse is $\"\"$ .

Co-vertices of the ellipse is $\"\"$

The distance between center and vertex is a.

The distance between center and focus is c.

The distance between center and co-vertex is b.

Condition is $\"\"$ .

Step 2:

The foci of the ellipse is $\"\"$ .

The co-vertices of the ellipse is $\"\"$ .

The distance between center and focus is $\"\"$ .

The distance between center and co-vertex is $\"\"$ .

Substitute $\"\"$ and $\"\"$ in $\"\"$ .

$\"\"$

Therefore the vertices of the ellipse is $\"\"$ .

Substitute $\"\"$ and $\"\"$ in vertical ellipse.

$\"\"$

Therefore the equation of the ellipse is $\"\"$ .

Solution :

The equation of the ellipse is $\"\"$ .