Divide each side by 18
x2/6 + y2/9 = 1
In this case, coefficient of y^2 > coefficient of x^2
Which is of the form x2/b2 + y2/a2 = 1
For general form of ellipse:
x2/b2 + y2/a2 = 1 ….(1)
On comparing given equation with (1), we get
a = 3 and b = √6
Then,
c2 = a2 – b2
c2 = 9 – 6 = 3
or c = √3
(i) Lengths of major and minor axes:
Major axis: 2a = 6 units
Minor axis : 2b = 2√6 units
(ii) Coordinates of the vertices: (0, ±a) = (0, ±3)
(iii) Coordinates of the foci: (0, ±c) = (0, ±√3)
(iv) Eccentricity: e = c/a = 1/√3
(v) Length of the latus rectum: 2b2/a = 4 units