NCERT Solutions for Class 11 Maths Chapter 10 Conic Sections Ex 10.3
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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 Class 11 Maths
Question 7.
36x2 + 4y2 = 144
Solution:
The given equation of ellipse is: 36x2 + 4y2 =
144
Ex 10.3 Class 11 Maths
Question 8.
16x2 + y2 = 16
Solution:
The given equation of ellipse is: 16x2 + y2 =
16
Ex 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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 10.3 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:
