We have been given an equation of ellipse

x2

36

+

y2

16

= 1
Clearly, 36 > 16
The equation of ellipse in standard form is

x2

a2

+

y2

b2

= 1
∴ a2 = 36 ⇒ a = 6 and b2 = 16 ⇒ b = 4
We know that
c = √a2−b2 ⇒ c = √36−16 = √20
∴ Coordinates of foci are (±c, 0) i.e. (± √20, 0)
Coordinates of vertices are (± a, 0) i.e. (± 6, 0).
Length of major axis = 2a = 2 × 6 = 12
Length of minor axis = 2b = 2 × 4 = 8
Eccentricity (e) =

c

a

=

√20

6

Length of latus rectum =

2b2

a

=

2×16

6

=

16

3