Find the equation of the ellipse whose foci are (4, 0) and (- 4, 0), eccentricity = 1/3.

Question

Philoid · Accepted Answer

Given that we need to find the equation of the ellipse whose eccentricity is and foci (±4,0).

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

We know that eccentricity(e) =

⇒

We know that foci = (±ae,0)

⇒ ae = 4

⇒

⇒ a = 12

⇒ a² = 144

⇒

⇒ b² = 128

The equation of the ellipse is

⇒

∴ The equation of the ellipse is .