Given equation of hyperbola is 9y2–4x2 = 36
i.e.,

9y2

36

−

4x2

36

= 1 ⇒

y2

4

−

x2

9

= 1 , which is of the form

y2

a2

−

x2

b2

= 1.
The foci and vertices of the hyperbola lie on y-axis.
Now, a2 = 4 ⇒ a = 2 and b2 = 9 ⇒ b = 3
Also, c2 = a2+b2 = 4 + 9 = 13 ⇒ c = √13
∴ Coordinates of foci are (0, ± c) i.e. (0, ± √13)
∴ Coordinates of vertices are (0, ±a) i.e. (0, ±2)
Eccentricity (e) =

c

a

=

√13

2

Length of latus rectum =

2b2

a

=

2×9

2

= 9.