find the equation of the ellipse in the following cases:

Foci (± 3, 0), a = 4

Given that we need to find the equation of the ellipse whose foci are (±3,0) and a = 4.

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

⇒ a = 4

⇒ a² = 16

We know that foci = (±ae,0)

⇒ ae = 3

⇒ 4e = 3

⇒

We know that eccentricity

⇒

⇒

⇒

⇒ b² = 7

The equation of the ellipse is

⇒

⇒

⇒ 7x² + 16y² = 112

∴ The equation of the ellipse is 7x² + 16y² = 112.