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 = 
4