Given equation of ellipse is 4x2+9y2 = 36
i.e.,

4x2 9y2

36

= 1 ⇒

x2

9

+

y2

4

= 1
Clearly, 9 > 4 ⇒ a2 = 9 and b2 = 4
The equation of ellipse in standard form is

x2

a2

+

y2

b2

= 1
∴ a2 = 9 ⇒ a = 3 and b2 = 4 ⇒ b = 2
We know that c = √a2−b2 ⇒ c = √9−4 = √5
∴ Coordinates of foci are (±c, 0) i.e. (± √5, 0)
Coordinates of vertices are (±a, 0) i.e. (±3, 0).
Length of major axis = 2a = 2 × 3 = 6
Length of minor axis = 2b = 2 × 2 = 4
Eccentricity (e) =

c

a

=

√5

3

Length of latus rectum =

2b2

a

=

2×4

3

=

8

3