# RD Sharma solutions for Class 11 Mathematics Textbook chapter 26 - Ellipse [Latest edition]

#### Chapters ## Chapter 26: Ellipse

Exercise 26.1Exercise 26.2Exercise 26.3
Exercise 26.1 [Pages 22 - 23]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 26 Ellipse Exercise 26.1 [Pages 22 - 23]

Exercise 26.1 | Q 1 | Page 22

Find the equation of the ellipse whose focus is (1, −2), the directrix 3x − 2y + 5 = 0 and eccentricity equal to 1/2.

Exercise 26.1 | Q 2.1 | Page 22

Find the equation of the ellipse in the case:

focus is (0, 1), directrix is x + y = 0 and e = $\frac{1}{2}$ .

Exercise 26.1 | Q 2.2 | Page 22

Find the equation of the ellipse in the case:

focus is (−1, 1), directrix is x − y + 3 = 0 and e = $\frac{1}{2}$

Exercise 26.1 | Q 2.3 | Page 22

Find the equation of the ellipse in the case:

focus is (−2, 3), directrix is 2x + 3y + 4 = 0 and e = $\frac{4}{5}$

Exercise 26.1 | Q 2.4 | Page 22

Find the equation of the ellipse in the case:

focus is (1, 2), directrix is 3x + 4y − 5 = 0 and e = $\frac{1}{2}$ Exercise 26.1 | Q 3.1 | Page 22

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:
4x2 + 9y2 = 1

Exercise 26.1 | Q 3.2 | Page 22

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

5x2 + 4y2 = 1

Exercise 26.1 | Q 3.3 | Page 22

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

4x2 + 3y2 = 1

Exercise 26.1 | Q 3.4 | Page 22

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

25x2 + 16y2 = 1600.

Exercise 26.1 | Q 3.5 | Page 22

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

9x2 + 25y2 = 225

Exercise 26.1 | Q 4 | Page 22

Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (−3, 1) and has eccentricity $\sqrt{\frac{2}{5}}$

Exercise 26.1 | Q 5.01 | Page 22

Find the equation of the ellipse in the case:

eccentricity e = $\frac{1}{2}$ and foci (± 2, 0)

Exercise 26.1 | Q 5.02 | Page 22

Find the equation of the ellipse in the case:

eccentricity e = $\frac{2}{3}$ and length of latus rectum = 5

Exercise 26.1 | Q 5.03 | Page 22

Find the equation of the ellipse in the case:

eccentricity e = $\frac{1}{2}$  and semi-major axis = 4

Exercise 26.1 | Q 5.04 | Page 22

Find the equation of the ellipse in the case:

eccentricity e = $\frac{1}{2}$  and major axis = 12

Exercise 26.1 | Q 5.05 | Page 22

Find the equation of the ellipse in the case:

The ellipse passes through (1, 4) and (−6, 1).

Exercise 26.1 | Q 5.06 | Page 22

Find the equation of the ellipse in the case:

Vertices (± 5, 0), foci (± 4, 0)

Exercise 26.1 | Q 5.07 | Page 22

Find the equation of the ellipse in the case:

Vertices (0, ± 13), foci (0, ± 5)

Exercise 26.1 | Q 5.08 | Page 22

Find the equation of the ellipse in the following case:

Vertices (± 6, 0), foci (± 4, 0)

Exercise 26.1 | Q 5.09 | Page 22

Find the equation of the ellipse in the following case:

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

Exercise 26.1 | Q 5.1 | Page 22

Find the equation of the ellipse in the following case:

Ends of major axis (0, ±$\sqrt{5}$ ends of minor axis (± 1, 0)

Exercise 26.1 | Q 5.11 | Page 22

Find the equation of the ellipse in the following case:

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

Exercise 26.1 | Q 5.12 | Page 22

Find the equation of the ellipse in the following case:

Length of minor axis 16 foci (0, ± 6)

Exercise 26.1 | Q 5.13 | Page 22

Find the equation of the ellipse in the following case:

Foci (± 3, 0), a = 4

Exercise 26.1 | Q 6 | Page 23

Find the equation of the ellipse whose foci are (4, 0) and (−4, 0), eccentricity = 1/3.

Exercise 26.1 | Q 7 | Page 23

Find the equation of the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is 10.

Exercise 26.1 | Q 8 | Page 23

Find the equation of the ellipse whose centre is (−2, 3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.

Exercise 26.1 | Q 9.1 | Page 23

Find the eccentricity of an ellipse whose latus rectum is  half of its minor axis

Exercise 26.1 | Q 9.2 | Page 23

Find the eccentricity of an ellipse whose latus rectum is  half of its major axis.

Exercise 26.1 | Q 10.1 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

x2 + 2y2 − 2x + 12y + 10 = 0

Exercise 26.1 | Q 10.2 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

x2 + 4y2 − 4x + 24y + 31 = 0

Exercise 26.1 | Q 10.3 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

4x2 + y2 − 8x + 2y + 1 = 0

Exercise 26.1 | Q 10.4 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

3x2 + 4y2 − 12x − 8y + 4 = 0

Exercise 26.1 | Q 10.5 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

4x2 + 16y2 − 24x − 32y − 12 = 0

Exercise 26.1 | Q 10.6 | Page 23

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

x2 + 4y2 − 2x = 0

Exercise 26.1 | Q 11 | Page 23

Find the equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).

Exercise 26.1 | Q 12 | Page 23

Find the equation of an ellipse whose eccentricity is 2/3, the latus-rectum is 5 and the centre is at the origin.

Exercise 26.1 | Q 13 | Page 23

Find the equation of an ellipse with its foci on y-axis, eccentricity 3/4, centre at the origin and passing through (6, 4).

Exercise 26.1 | Q 14 | Page 23

Find the equation of an ellipse whose axes lie along coordinate axes and which passes through (4, 3) and (−1, 4).

Exercise 26.1 | Q 15 | Page 23

Find the equation of an ellipse whose axes lie along the coordinate axes, which passes through the point (−3, 1) and has eccentricity equal to $\sqrt{2/5}$

Exercise 26.1 | Q 16 | Page 23

Find the equation of an ellipse, the distance between the foci is 8 units and the distance between the directrices is 18 units.

Exercise 26.1 | Q 17 | Page 23

Find the equation of an ellipse whose vertices are (0, ± 10) and eccentricity e = $\frac{4}{5}$

Exercise 26.1 | Q 18 | Page 23

A rod of length 12 m moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with x-axis.

Exercise 26.1 | Q 19 | Page 23

Find the equation of the set of all points whose distances from (0, 4) are$\frac{2}{3}$ of their distances from the line y = 9.

Exercise 26.2 [Page 27]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 26 Ellipse Exercise 26.2 [Page 27]

Exercise 26.2 | Q 1 | Page 27

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and $\sqrt{3}$ and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse.

Exercise 26.2 | Q 2 | Page 27

Write the eccentricity of the ellipse 9x2 + 5y2 − 18x − 2y − 16 = 0.

Exercise 26.2 | Q 3 | Page 27

Write the centre and eccentricity of the ellipse 3x2 + 4y2 − 6x + 8y − 5 = 0.

Exercise 26.2 | Q 4 | Page 27

PSQ is a focal chord of the ellipse 4x2 + 9y2 = 36 such that SP = 4. If S' is the another focus, write the value of S'Q

Exercise 26.2 | Q 5 | Page 27

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

Exercise 26.2 | Q 6 | Page 27

If the distance between the foci of an ellipse is equal to the length of the latus-rectum, write the eccentricity of the ellipse.

Exercise 26.2 | Q 7 | Page 27

If S and S' are two foci of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ and B is an end of the minor axis such that ∆BSS' is equilateral, then write the eccentricity of the ellipse.

Exercise 26.2 | Q 8 | Page 27

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse.

Exercise 26.2 | Q 9 | Page 27

If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.

Exercise 26.3 [Pages 27 - 29]

### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 26 Ellipse Exercise 26.3 [Pages 27 - 29]

Exercise 26.3 | Q 1 | Page 27

For the ellipse 12x2 + 4y2 + 24x − 16y + 25 = 0

• centre is (−1, 2)

•  lengths of the axes are $\sqrt{3}$ and 1

• eccentricity = sqrt(2/3)

• all of these

Exercise 26.3 | Q 2 | Page 28

The equation of the ellipse with focus (−1, 1), directrix x − y + 3 = 0 and eccentricity 1/2 is

Exercise 26.3 | Q 3 | Page 28

The equation of the circle drawn with the two foci of $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ as the end-points of a diameter is

• x2 + y2 = a2 + b2

• x2 + y2 = a2

• x2 + y2 = 2a2

• x2 + y2 = a2 − b2

Exercise 26.3 | Q 4 | Page 28

The eccentricity of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ if its latus rectum is equal to one half of its minor axis, is

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

• none of these

Exercise 26.3 | Q 5 | Page 28

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

• $\frac{\sqrt{5} - 1}{2}$

• $\frac{\sqrt{5} + 1}{2}$

• $\frac{\sqrt{5} - 1}{4}$

• none of these

Exercise 26.3 | Q 6 | Page 28

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

• $\frac{\sqrt{3}}{2}$

• $\frac{2}{\sqrt{3}}$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{2}}{3}$

Exercise 26.3 | Q 7 | Page 28

The difference between the lengths of the major axis and the latus-rectum of an ellipse is

• ae

• 2ae

• ae2

• 2ae2

Exercise 26.3 | Q 8 | Page 28

The eccentricity of the conic 9x2 + 25y2 = 225 is

• 2/5

• 4/5

• 1/3

• 1/5

• 3/5

Exercise 26.3 | Q 9 | Page 28

The latus-rectum of the conic 3x2 + 4y2 − 6x + 8y − 5 = 0 is

• 3

• $\frac{\sqrt{3}}{2}$

• $\frac{2}{\sqrt{3}}$

• none of these

Exercise 26.3 | Q 10 | Page 28

The equations of the tangents to the ellipse 9x2 + 16y2 = 144 from the point (2, 3) are

•  y = 3, x = 5

•  x = 2, y = 3

• x = 3, y = 2

•  x + y = 5, y = 3

Exercise 26.3 | Q 11 | Page 28

The eccentricity of the ellipse 4x2 + 9y2 + 8x + 36y + 4 = 0 is

• $\frac{5}{6}$

• $\frac{3}{5}$

• $\frac{\sqrt{2}}{3}$

• $\frac{\sqrt{5}}{3}$

Exercise 26.3 | Q 12 | Page 28

The eccentricity of the ellipse 4x2 + 9y2 = 36 is

• $\frac{1}{2\sqrt{3}}$

• $\frac{1}{\sqrt{3}}$

• $\frac{\sqrt{5}}{3}$

• $\frac{\sqrt{5}}{6}$

Exercise 26.3 | Q 13 | Page 28

The eccentricity of the ellipse 5x2 + 9y2 = 1 is

• 2/3

•  3/4

• 4/5

• 1/2

Exercise 26.3 | Q 14 | Page 28

For the ellipse x2 + 4y2 = 9

• the eccentricity is 1/2

• the latus-rectum is 3/2

• a focus is $\left( 3\sqrt{3}, 0 \right)$

•  a directrix is x = $- 2\sqrt{3}$

Exercise 26.3 | Q 15 | Page 29

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{3}}{2}$

• $\frac{\sqrt{3}}{4}$

Exercise 26.3 | Q 16 | Page 29

An ellipse has its centre at (1, −1) and semi-major axis = 8 and it passes through the point (1, 3). The equation of the ellipse is

• $\frac{\left( x + 1 \right)^2}{64} + \frac{\left( y + 1 \right)^2}{16} = 1$

• $\frac{\left( x - 1 \right)^2}{64} + \frac{\left( y + 1 \right)^2}{16} = 1$

• $\frac{\left( x - 1 \right)^2}{16} + \frac{\left( y + 1 \right)^2}{64} = 1$

• $\frac{\left( x + 1 \right)^2}{64} + \frac{\left( y - 1 \right)^2}{16} = 1$

Exercise 26.3 | Q 17 | Page 29

The sum of the focal distances of any point on the ellipse 9x2 + 16y2 = 144 is

• 32

• 18

• 16

• 8

Exercise 26.3 | Q 18 | Page 29

If (2, 4) and (10, 10) are the ends of a latus-rectum of an ellipse with eccentricity 1/2, then the length of semi-major axis is

• 20/3

• 15/3

• 40/3

• none of these

Exercise 26.3 | Q 19 | Page 29

The equation $\frac{x^2}{2 - \lambda} + \frac{y^2}{\lambda - 5} + 1 = 0$ represents an ellipse, if

•  λ < 5

• λ < 2

• 2 < λ < 5

• λ < 2 or λ > 5

Exercise 26.3 | Q 20 | Page 29

The eccentricity of the ellipse 9x2 + 25y2 − 18x − 100y − 116 = 0, is

• 25/16

• 4/5

• 16/25

• 5/4

Exercise 26.3 | Q 21 | Page 29

If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to

• $\frac{1}{3}$

• $\frac{1}{\sqrt{3}}$

• $\frac{1}{\sqrt{2}}$

• $\frac{2\sqrt{2}}{3}$

• $\frac{2}{3\sqrt{2}}$

Exercise 26.3 | Q 22 | Page 29

The eccentricity of the ellipse 25x2 + 16y2 = 400 is

• 3/5

• 1/3

•  2/5

• 1/5

Exercise 26.3 | Q 23 | Page 29

The eccentricity of the ellipse 5x2 + 9y2 = 1 is

• 2/3

• 3/4

•  4/5

• 1/2

Exercise 26.3 | Q 24 | Page 29

The eccentricity of the ellipse 4x2 + 9y2 = 36 is

• $\frac{1}{2\sqrt{3}}$

• $\frac{1}{\sqrt{3}}$

• $\frac{\sqrt{5}}{3}$

• $\frac{\sqrt{5}}{6}$

## Chapter 26: Ellipse

Exercise 26.1Exercise 26.2Exercise 26.3 ## RD Sharma solutions for Class 11 Mathematics Textbook chapter 26 - Ellipse

RD Sharma solutions for Class 11 Mathematics Textbook chapter 26 (Ellipse) include all questions with solution and detail explanation. This will clear students doubts about any question and improve application skills while preparing for board exams. The detailed, step-by-step solutions will help you understand the concepts better and clear your confusions, if any. Shaalaa.com has the CBSE Class 11 Mathematics Textbook solutions in a manner that help students grasp basic concepts better and faster.

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Concepts covered in Class 11 Mathematics Textbook chapter 26 Ellipse are Sections of a Cone, Concept of Circle, Introduction of Parabola, Standard Equations of Parabola, Latus Rectum, Introduction of Ellipse, Relationship Between Semi-major Axis, Semi-minor Axis and the Distance of the Focus from the Centre of the Ellipse, Special Cases of an Ellipse, Standard Equations of an Ellipse, Latus Rectum, Introduction of Hyperbola, Eccentricity, Standard Equation of Hyperbola, Latus Rectum, Standard Equation of a Circle, Eccentricity.

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