Given equation is of the form y2/a2 – x2/b2 = 1
On comparing given equation with (2), we get
a = 3 and b = √27 = 3√3
Then,
c2 = a2 + b2
c2 = 9 + 27 = 36
or c = 6
Now,
(i) Lengths of the axes:
Length of Transverse axis = 2a = 6 units
Length of Conjugate axis = 2b = 6√3 units
(ii) Coordinates of the vertices: (0, ±a) = (0, ±3)
(iii) Coordinates of the foci: (0, ±c) = (0, ±6)
(iv) Eccentricity: e = c/a = 2
(v) Length of the latus rectum: 2b2/a = 18 units