Find the equation for the ellipse that satisfies the given conditions: Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and (1,6).

= 1

Given that the points(3, 2) and (1, 6) lie on the ellipse, we have

= 1 and = 1

or 9a² + 4b² = a²b²

and a² + 36b² = a²b²

or 9a² + 4b² = a²b²

and 9a² + 324b² = 9a²b²

On subtracting we get

ca² + 4b² = a²b²

9a² + 324b² = 9a²b²

- - ; ; -

- 320b² = -8a²b²

or a² = 40

Hence, the required equation is of form

= 1

To find b² we substitute a² = 40 in = 1

or = 1

or

or

or b² = 10

Hence the equation of the given ellipse is

= 1