NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3

NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3 are the part of NCERT Solutions for Class 11 Maths. Here you can find the NCERT Solutions for Class 11 Maths Chapter 11 Conic Sections Ex 11.3.


In each of the Exercises 1 to 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.

Ex 11.3 Class 11 Maths Question 1.

x2/36 + y2/16 = 1

Solution:
The given equation of ellipse is: x2/36 + y2/16 = 1
Clearly, 36 > 16
The equation of ellipse in standard form is:


 

Ex 11.3 Class 11 Maths Question 2.

x2/4 + y2/25 = 1

Solution:
The given equation of ellipse is: x2/4 + y2/25 = 1
Clearly, 25 > 4
The equation of ellipse in standard form is:

 

Ex 11.3 Class 11 Maths Question 3.

x2/16 + y2/9 = 1

Solution:
The given equation of ellipse is: x2/16 + y2/9 = 1
Clearly, 16 > 9
Here, a2 = 16 a = 4 and b2 = 9 b = 3.
Major axis is along x-axis.
Also, c2 = a2 – b2 = 16 – 9 = 7
c = 7
Coordinates of foci (±c, 0), i.e., (±7, 0).
Vertices are (±a, 0), i.e., (±4, 0).
Length of major axis = 2a = 2 × 4 = 8.
Length of minor axis = 2b = 2 × 3 = 6.

Eccentricity e = c/a = 7/4
Also, Latus rectum = 2b2/a = (2×9)/4 = 9/2.

 

Ex 11.3 Class 11 Maths Question 4.

x2/25 + y2/100 = 1

Solution:
The given equation of ellipse is: x2/25 + y2/100 = 1
Clearly, 100 > 25
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 5.

x2/49 + y2/36 = 1

Solution:
The given equation of ellipse is: x2/49 + y2/36 = 1
Clearly, 49 > 36
The equation of ellipse in standard form is:


 

Ex 11.3 Class 11 Maths Question 6.

x2/100 + y2/400 = 1

Solution:
The given equation of ellipse is: x2/100 + y2/400 = 1
Clearly, 400 > 100
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 7.

36x2 + 4y2 = 144

Solution:
The given equation of ellipse is: 36x2 + 4y2 = 144

Ex 11.3 Class 11 Maths Question 8.

16x2 + y2 = 16

Solution:
The given equation of ellipse is: 16x2 + y2 = 16


Ex 11.3 Class 11 Maths Question 9.

4x2 + 9y2 = 36

Solution:
The given equation of ellipse is: 4x2 + 9y2 = 36


In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions:

Ex 11.3 Class 11 Maths Question 10.

Vertices (±5, 0), foci (±4, 0)

Solution:
Clearly, the foci (±4, 0) lie on the x-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 11.

Vertices (0, ±13), foci (0, ±5)

Solution:
Clearly, the foci (0, ±5) lie on the y-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 12.

Vertices (±6, 0), foci (±4, 0)

Solution:
Clearly, the foci (±4, 0) lie on the x-axis.

The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 13.

Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Solution:
Since, ends of major axis (±3, 0) lie on the x-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 14.

Ends of major axis (0, ±5), ends of minor axis (±1, 0)

Solution:
Since, ends of major axis (0, ±5) lie on y-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 15.

Length of major axis 26, foci (±5, 0)

Solution:
Since the foci (±5, 0) lie on the x-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 16.

Length of minor axis 16, foci (0, ±6)

Solution:
Since the foci (0, ±6) lie on y-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 17.

Foci (±3, 0), a = 4

Solution:
Since the foci (±3, 0) lie on the x-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 18.

b = 3, c = 4, centre at the origin; foci on the x-axis.

Solution:
Since the foci lie on the x-axis.
The equation of ellipse in standard form is:


Ex 11.3 Class 11 Maths Question 19.

Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Solution:
Since the major axis is along the y-axis.
The equation of ellipse in standard form is:

Ex 11.3 Class 11 Maths Question 20.

Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

Solution:
Since the major axis is along the x-axis.
The equation of ellipse in standard form is:


You can also like these:

NCERT Solutions for Maths Class 9

NCERT Solutions for Maths Class 10

NCERT Solutions for Maths Class 12

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