Given equation of ellipse is

x2

100

+

y2

400

= 1
Clearly, 400 > 100
The equation of ellipse in standard form is

y2

a2

+

x2

b2

= 1
∴ a2 = 400 ⇒ a = 20 and b2 = 100 ⇒ b = 10
We know that
c = √a2−b2 ⇒ c = √400−100 = √300 = 10√3
∴ Coordinates of foci are (0, ± c) i.e. (0, ± 10 √3)
Coordinates of vertices are (0, ± a) i.e. (0, ± 20).
Length of major axis = 2a = 2 × 20 = 40
Length of minor axis = 2b = 2 × 10 = 20
Eccentricity (e) =

c

a

=

10√3

20

=

√3

2

Length of latus rectum =

2b2

a

=

2×100

20

= 10.