Divide both sides by 225
x2/9 – y2/25 = 1
Given equation is of the form x2/a2 – y2/b2 = 1
On comparing given equation with (1), we get
a = 3 and b = 5
Then,
c2 = a2 + b2
c2 = 9 + 25 = 34
or c = √34
Now,
(i) Lengths of the axes:
Length of Transverse axis = 2a = 6 units
Length of Conjugate axis = 2b = 10 units
(ii) Coordinates of the vertices: (±a, 0) = (±3, 0)
(iii) Coordinates of the foci: (±c, 0) = (±√34, 0)
(iv) Eccentricity: e = c/a = √34/3
(v) Length of the latus rectum: 2b2/a = 50/3 units