Find the equation for the ellipse that satisfies the given conditions: centre at the origin; foci on the - axis.
Solution: It is given that , centre at the origin; foci on the - axis.
Since the foci are on the -axis the major axis is along the -axis.
Therefore, the equation of the ellipse will be of the form where is the semi-major axis.
It is known that
Thus, the equation of the ellipse is