Since the center is at (0,0) and the major axis is on the y- axis, the equation of the ellipse will be of the form

=1 ………………….(1)

Where, a is the semi - major axis

The ellipse passes through points (3, 2) and (1, 6). Hence,

=1 …………………… (2)

=1……………………… (3)

On solving equation (2) and (3), we obtain b² = 10 and a² = 40.

Thus, the equation of the ellipse is = 1 or 4x² + y ² = 40.