Chapter 11 – Conic Sections (Ex – 11.3)

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.

Question 1.
x²/36 + y²/16 = 1

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

Question 2.
x²/4 + y²/25 = 1

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

Question 3.
x²/16 + y²/9 = 1

Solution:
Given equation of ellipse is x²/16 + y²/9 = 1
Clearly, 16 > 9
The equation of ellipse in standard form is

Question 4.
x²/25 + y²/100 = 1
Solution:
Given equation of ellipse is x²/25 + y²/100 = 1
Clearly, 100 > 25
The equation of ellipse in standard form is

Question 5.
x²/49 + y²/36 = 1

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

Question 6.
x²/16 + y²/9 = 1

Solution:
Given equation of ellipse is x²/16 + y²/9 = 1
Clearly, 400 > 100
The equation of ellipse in standard form is

Question 7.
36x² + 4y² = 144

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

Question 8.
16x² + y² = 16

Solution:
Given equation of ellipse is16x² + y² = 16

Question 9.
4x² + 9y² = 36

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

In each 0f the following Exercises 10 to 20, find the equation for the ellipse that satisfies the given conditions:

Question 10.
Vertices (±5, 0), foci (±4,0)

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

Question 11.
Vertices (0, ±13), foci (0, ±5)

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

Question 12.
Vertices (±6, 0), foci (±4,0)

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

Question 13.
Ends of major axis (±3, 0), ends of minor axis (0, ±2)

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

Question 14.
Ends of major axis (0, ±√5), ends of minor axis (±1, 0)

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

Question 15.
Length of major axis 26, foci (±5, 0)

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

Question 16.
Length of major axis 16, foci (0, ±6)

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

Question 17.
Foci (±3, 0) a = 4

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

Question 18.
b = 3, c = 4, center at the origin; foci on the x axis.

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

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 y-axis.
∴ The equation of ellipse in standard form

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