CLASS_11_MATHS_SOLUTIONS_NCERT

Class XI Chapter 11 – Conic Section Maths
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2 2
c a b
16 1 15
Therefore,
The coordinates of the foci are0, 15 .
The coordinates of the vertices are (0, ±4).
Length of major axis = 2a= 8
Length of minor axis = 2b= 2
c 15
Eccentricity, e= a 4
Length of latus rectum
2
2b
21 1
a 4 2
Question 9:
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the
eccentricity and the length of the latus rectum of the ellipse 4x 2 + 9y 2 = 36
Solution 9:
The given equation is 4x 2 + 9y 2 = 36.
It can be written as
2 2
4x
9y
36
2 2
x y
Or, 1
9 4
2 2
x y
Or, 1 ....
2 2
1
3 2
2
2
x
Here, the denominator of
2
3 is greater than the denominator of y
2 .
2
Therefore, the major axis is along the x-axis, while the minor axis is along the y-axis.
2 2
x y
On comparing the given equation with 1 , we obtain a = 3 and b = 2.
2 2
b a
2 2
c a b
9 4 5
Therefore,
The coordinates of the foci are 5,0
.
The coordinates of the vertices are ( ±3, 0).
Length of major axis = 2a= 6
Length of minor axis = 2b= 4
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