Step 1:

The points are $\"\"$ .

Let $\"\"$

The length of the major axis is $\"\"$ .

$\"\"$

The center of the ellipse is the average between two points.

$\"\"$

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

Step 2:

The distance from center to one of the foci is $\"\"$ .

The foci is lie on the major axis, $\"\"$ units from the center is,

$\"\"$

The standard form of the equation of ellipse with major axis is vertical,

$\"\"$ .

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

$\"\"$

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

Solution :

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