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