Find the eccentricity, coordinates of foci, length of the latus - rectum of the following ellipse:

25x² + 16y² = 1600

Given the equation of the ellipse is 25x² + 16y² = 1600.

We need to find the eccentricity, coordinates of foci and length of latus rectum.

Given equation can be rewritten as

⇒ .

We know for the ellipse (b²>a²)

⇒

⇒ Coordinates of foci (0,±be)

⇒ Length of latus rectum =

Here a² = 64 and b² = 100, b²>a²

⇒

⇒

⇒

⇒

⇒

⇒ foci = (0,±6)

⇒ Length of latus rectum (L) =

⇒

∴ The eccentricity is , foci are (0,±6) and length of the latus rectum is .