Question

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).

Answer 1

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

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

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

Thus, the equation of the ellipse is.