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.
49y2 – 16x2 = 784.
The given equation is 49y2 – 16x2 = 784
We can re-write the given as
Or 
……….. (1)
On comparing this equation (1) with the standard equation of hyperbola
, we get,
a = 4 and b =7
We know, a2 + b2 = c2
Thus,
c2 = 16 + 49 = 65
⇒ c = 
Therefore,
The coordinates of the foci are (0, 
).
The coordinates of the vertices are (0, 
4).
Eccentricity, e = 
Length of latus rectum = 
7