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 = 
4