Divide each side by 36, we get
y2/(36/5) – x2/4 = 1
Which is of the form y2/a2 – x2/b2 = 1
On comparing given equation with (2), we get
a = 6/√5 and b = 2
Then,
c2 = a2 + b2
c2 = 36/5 + 4 = 56/5
or c = 2√(14/5)
Now,
(i) Lengths of the axes:
Length of Transverse axis = 2a = 12/√5 units
Length of Conjugate axis = 2b = 4 units
(ii) Coordinates of the vertices: (0, ±a) = (0, ±6/√5)
(iii) Coordinates of the foci: (0, ±c) = (0, ±2√(14/5))
(iv) Eccentricity: e = c/a = √14/3
(v) Length of the latus rectum: 2b2/a = 4√5/3 units