Divide each side by 108
y2/36 – x2/108 = 1
Which is of the form y2/a2 – x2/b2 = 1
On comparing given equation with (2), we get
a = 6 and b = 6√3
Then,
c2 = a2 + b2
c2 = 36 + 108 = 144
or c = 12
Now,
(i) Lengths of the axes:
Length of Transverse axis = 2a = 12 units
Length of Conjugate axis = 2b = 12√3 units
(ii) Coordinates of the vertices: (0, ±a) = (0, ±6)
(iii) Coordinates of the foci: (0, ±c) = (0, ±12)
(iv) Eccentricity: e = c/a = 2
(v) Length of the latus rectum: 2b2/a = 36 units