Given that we need to find the equation of the ellipse whose vertices are (±5,0) and foci (±4,0).

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

We know that vertices of the ellipse are (±a,0)

⇒ a = 5

⇒ a² = 25

We know that foci = (±ae,0)

⇒ ae = 4

⇒ 5e = 4

⇒

We know that eccentricity

⇒

⇒

⇒

⇒ b² = 9

The equation of the ellipse is

⇒

⇒

⇒ 9x² + 25y² = 225

∴ The equation of the ellipse is 9x² + 25y² = 225.