Given equation of ellipse is

x2

25

+

y2

100

= 1
Clearly, 100 > 25
The equation of ellipse in standard form is

y2

a2

+

x2

b2

= 1
∴ a2 = 100 ⇒ a = 10 and b2 = 25 ⇒ b = 5
We know that c = √a2−b2 ⇒ c = √100−25 = √75 = 5√3
∴ Coordinates of foci are (0, ±c) i.e. (0, ± 5 √3)
Coordinates of vertices are (0, ±a) i.e. (0, ±10).
Length of major axis = 2a = 2 × 10 = 20
Length of minor axis = 2b = 2 × 5 = 10
Eccentricity (e) =

c

a

=

5√3

10

=

√3

2

Length of latus rectum =

2b2

a

=

2×25

10

= 5.