Given equation of hyperbola is

y2

9

−

x2

27

= 1 which is of the form

y2

a2

−

x2

b2

= 1.
The foci and vertices of the hyperbola lie on y-axis.
Now, a2 = 9 ⇒ a = 3 and b2 = 27 ⇒ b = 3 √3
Also, c2 = a2+b2 = 9 + 27 = 36 ⇒ c = 6
So, coordinates of foci are (0, ±c) i.e. (0, ±6)
Coordinates of vertices are (0, ±a) i.e. (0, ±3)
Eccentricity (e) =

c

a

=

6

3

= 2
Length of latus rectum =

2b2

a

=

2×27

3

= 18.