In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

16x² – 9y² = 576

The given equation is 16y² – 9x² = 576

We can re-write the given as

Or ……….. (1)

On comparing this equation (1) with the standard equation of hyperbola

, we get,

a = 6 and b =8

We know, a² + b² = c²

Thus,

c² = 36 + 64 = 100

⇒ c = 10

Therefore,

The coordinates of the foci are (10, 0).

The coordinates of the vertices are (6, 0).

Eccentricity, e =

Length of latus rectum =