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.

9y² – 4x² = 36

The given equation is 9y² – 4x² = 36

We can re-write the given as

or ………..(1)

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

, we get,

a = 2 and b =3

We know, a² + b² = c²

Thus,

c² = 4 + 9 = 13

⇒ c =

Therefore,

The coordinates of the foci are (0, ).

The coordinates of the vertices are (0, 2).

Eccentricity, e =

Length of latus rectum =