Question -
Answer -
Given:
The equation is 4x2 +9y2 = 36 or x2/9 + y2/4= 1 or x2/32 +y2/22 =1
Here, the denominator of x2/32 is greater than the denominator of y2/22.
So, the major axis is along the x-axis, while the minor axis isalong the y-axis.
On comparing the given equation with x2/a2 +y2/b2 =1, we get
a =3 and b =2.
c = √(a2 – b2)
= √(9-4)
= √5
Then,
The coordinates of the foci are (√5, 0) and (-√5, 0).
The coordinates of the vertices are (3, 0) and (-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= (2×22)/3 = (2×4)/3 = 8/3