Given equation of ellipse is 36x2+4y2 = 144
i.e.,

36x2

144

+

4y2

144

= 1 ⇒

x2

4

+

y2

36

= 1
Clearly, 36 > 4
The equation of ellipse in standard form is

y2

a2

+

x2

b2

= 1
∴ a2 = 36 ⇒ a = 6 and b2 = 4 ⇒ b = 2
We know that c = √a2−b2 ⇒ c = √36−4 = √32 = 4√2
∴ Coordinates of foci are (0, ± c)
i.e. (0, ± 4 √2)
Coordinates of vertices are (0, ± a) i.e. (0, ± 6).
Length of major axis = 2a = 2 × 6 = 12
Length of minor axis = 2b = 2 × 2 = 4
Eccentricity (e) =

c

a

=

4√2

6

=

2√2

3

Length of latus rectum =

2b2

a

=

2×4

6

=

4

3