Find the equation for the ellipse that satisfies the given conditions: Centre at , major axis on the -axis and passes through the points and
Solution: Since the centre is at and the major axis is on the -axi,s the equation of the ellipse will be of the form,
where is the semi-major axis.
The ellipse passes through points and .
On solving equations (2) and (3), we obtain and
Thus the equation of the ellipse is or