Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (- 3, 1) and has eccentricity.

Given that we need to find the equation of the ellipse (whose axes are x = 0 and y = 0) which passes through the point (- 3,1) and has eccentricity .

We know that the equation of the ellipse whose axes are x and y - axis is . ..... - - - - - (1)

Let us assume a²>b².

We know that eccentricity(e) =

⇒

⇒

⇒

⇒ ..... .... (2)

Substituting (2) in (1) we get,

⇒

⇒

⇒ 3x² + 5y² = 3a²

This curve passes through the point (- 3,1). Substituting in the curve we get,

⇒ 3(- 3)² + 5(1)² = 3a²

⇒ 3(9) + 5 = 3a²

⇒ 32 = 3a²

⇒

⇒

⇒

The equation of the ellipse is:

⇒

⇒

⇒ 3x² + 5y² = 32

∴ The equation of the ellipse is 3x² + 5y² = 32.