Divide both sides by 100
x2/100 + y2/25 = 1
For general form of ellipse:
x2/a2 + y2/b2 = 1 ….(1)
On comparing given equation with (1), we get
a = 10 and b = 5
Then,
c2 = a2 – b2
c2 = 100 – 25 = 75
or c = 5 √3
Now,
(i) Lengths of major and minor axes:
Major axis: 2a = 20 units
Minor axis : 2b = 10 units
(ii) Coordinates of the vertices: (±a, 0) = (±10, 0)
(iii) Coordinates of the foci: (±c, 0) = (±5 √3, 0)
(iv) Eccentricity: e = c/a = 5√3/10 = √3/2
(v) Length of the latus rectum: 2b2/a = 2(5)2/10 = 5 units