Given that we need to find the equation of the ellipse whose eccentricity is and the semi - major axis is 4.

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

We know that eccentricity(e) =

⇒

⇒

⇒

⇒

We know that the length of the semi - major axis is a

⇒ a = 4

⇒ a² = 16

⇒

⇒ b² = 12

The equation of the ellipse is

⇒

⇒

⇒ 3x² + 4y² = 48

∴ The equation of the ellipse is 3x² + 4y² = 48.