Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4,3) and (6,2).

= 1 and = 1

or 16b² + 9a² = a²b²

and 36b² + 4a² = a²b²

or 64b² + 36a² = 4a²b²

and 324b² + 36a² = 9a²b²

On subtracting we get

64b² + 36a² = 4a²b²

324b² + 36a² = 9a²b²

- - -

260b² = -5a²b²

To find b² we substitute a² – 52 in = 1

or ; = 1 ⇒

or ; or b² = 13

Hence, the required equation is = 1.