Given that we need to find the equation of the ellipse whose minor axis is equal to the distance between foci and length of latus rectum is 10.

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

We know that length of the minor axis is 2b and distance between the foci is 2ae.

We know that eccentricity

⇒ 2b = 2ae

⇒ b = ae

⇒

⇒ b² = a² - b²

⇒ a² = 2b² ..... - - - - (1)

We know that the length of the latus rectum is .

⇒

From (1)

⇒

⇒ a = 10

⇒ a² = 100

⇒

⇒ b² = 50

The equation of the ellipse is

⇒

⇒

⇒ x² + 2y² = 100

∴ The equation of the ellipse is x² + 2y² = 100.