Find the equation of an ellipse whose axes lie along coordinates axes and which passes through (4, 3) and (- 1, 4).

Given that we need to find the equation of the ellipse passing through the points (4,3) and (- 1,4).

Let us assume the equation of the ellipse as (a²>b²). - - - - (1)

Substituting the point (4,3) in (1) we get

⇒

⇒

⇒

⇒ 16b² + 9a² = a² b² ..... - - (2)

Substituting the point (- 1,4) in (1) we get

⇒

⇒

⇒

⇒ b² + 16a² = a²b² ..... - - (3)

(3)×16 - (2)

⇒ (16b² + 256a²) - (9a² + 16b²) = (16a²b² - a²b²)

⇒ 247a² = 15a²b²

⇒ 15b² = 247

⇒

From (3)

⇒

⇒

⇒

⇒

The equation of the ellipse is

⇒

⇒

⇒ 7x² + 15y² = 247

∴ The equation of the ellipse is 7x² + 15y² = 247.