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.

5y2 – 9x2 = 36


The given equation is 5y2 – 9x2 = 36


We can re-write the given as


Or ……….. (1)


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


, we get,


a = and b =2


We know, a2 + b2 = c2


Thus,


c2 = =


c =


Therefore,


The coordinates of the foci are


The coordinates of the vertices are .


Eccentricity, e =


Length of latus rectum =


5
1