# 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.

Question 1.

$\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 16 } =1$

Solution:

Given equation of ellipse of $\frac { { x }^{ 2 } }{ 36 } +\frac { { y }^{ 2 } }{ 16 } =1$

Clearly, 36 > 16

The equation of ellipse in standard form is

Question 2.

$\frac { { x }^{ 2 } }{ 4 } +\frac { { y }^{ 2 } }{ 25 } =1$

Solution:

Given equation of ellipse is $\frac { { x }^{ 2 } }{ 4 } +\frac { { y }^{ 2 } }{ 25 } =1$

Clearly, 25 > 4

The equation of ellipse in standard form is

Question 3.

$\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$

Solution:

Given equation of ellipse is $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$

Clearly, 16 > 9

The equation of ellipse in standard form is

Question 4.

$\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 100 } =1$

Solution:

Given equation of ellipse is $\frac { { x }^{ 2 } }{ 25 } +\frac { { y }^{ 2 } }{ 100 } =1$

Clearly, 100 > 25

The equation of ellipse in standard form is

Question 5.

$\frac { { x }^{ 2 } }{ 49 } +\frac { { y }^{ 2 } }{ 36 } =1$

Solution:

Given equation of ellipse is $\frac { { x }^{ 2 } }{ 49 } +\frac { { y }^{ 2 } }{ 36 } =1$

Clearly, 49 > 36

The equation of ellipse in standard form is

Question 6.

$\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$

Solution:

Given equation of ellipse is $\frac { { x }^{ 2 } }{ 16 } +\frac { { y }^{ 2 } }{ 9 } =1$

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 is4x2 + 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, $\pm \sqrt { 5 }$), ends of minor axis (±1, 0)

Solution:

Since, ends of major axis (0, $\pm \sqrt { 5 }$) 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, centre 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