Given that we need to find the equation of the ellipse whose vertices are (0,±10) and eccentricity .

Let us assume the equation of the ellipse as - - - - (1) (a²>b²).

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

⇒ b = 10

⇒ b² = 100

We know that eccentricity

⇒

⇒

⇒

⇒

The equation of the ellipse is

⇒

⇒

⇒

⇒ 9x² + 25y² = 2500

∴ The equation of the ellipse is 9x² + 25y² = 2500.