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RD Sharma solutions for Class 11 Mathematics chapter 26 - Ellipse

Mathematics Class 11

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Chapters

RD Sharma Mathematics Class 11

Mathematics Class 11

Chapter 26: Ellipse

Chapter 26: Ellipse solutions [Pages 22 - 23]

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.

 
Q 2.1 | Page 22

Find the equation of the ellipse in the case: 

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

 

 

Q 2.2 | Page 22

Find the equation of the ellipse in the case: 

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

 
 

 

Q 2.3 | Page 22

Find the equation of the ellipse in the case: 

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

 
 

 

Q 2.4 | Page 22

Find the equation of the ellipse in the case: 

(iv) focus is (1, 2), directrix is 3x + 4y − 5 = 0 and e = \[\frac{1}{2}\]

 

 

Q 3.1 | Page 22

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

Q 3.2 | Page 22

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

(ii) 5x2 + 4y2 = 1

Q 3.3 | Page 22

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

(iii) 4x2 + 3y2 = 1

Q 3.4 | Page 22

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

(iv) 25x2 + 16y2 = 1600.

Q 3.5 | Page 22

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

(v) 9x2 + 25y2 = 225

 
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 \[\sqrt{\frac{2}{5}}\]

 
Q 5.01 | Page 22

Find the equation of the ellipse in the case:

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

Q 5.02 | Page 22

Find the equation of the ellipse in the case:

(ii) eccentricity e = \[\frac{2}{3}\] and length of latus rectum = 5

 
Q 5.03 | Page 22

Find the equation of the ellipse in the case: 

(iii) eccentricity e = \[\frac{1}{2}\]  and semi-major axis = 4

 
Q 5.04 | Page 22

Find the equation of the ellipse in the case:

(iv) eccentricity e = \[\frac{1}{2}\]  and major axis = 12

 

 

Q 5.05 | Page 22

Find the equation of the ellipse in the case:

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

Q 5.06 | Page 22

Find the equation of the ellipse in the case:

(vi) Vertices (± 5, 0), foci (± 4, 0)

Q 5.07 | Page 22

Find the equation of the ellipse in the case:

(vii) Vertices (0, ± 13), foci (0, ± 5)

 

Q 5.08 | Page 22

Find the equation of the ellipse in the following case: 

Vertices (± 6, 0), foci (± 4, 0) 

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) 

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) 

Q 5.11 | Page 22

Find the equation of the ellipse in the following case: 

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

Q 5.12 | Page 22

Find the equation of the ellipse in the following case:  

Length of minor axis 16 foci (0, ± 6)

 

Q 5.13 | Page 22

Find the equation of the ellipse in the following case:  

Foci (± 3, 0), a = 4

Q 6 | Page 23

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

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. 

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.

Q 9.1 | Page 23

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

Q 9.2 | Page 23

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

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 

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 

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 

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 

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 

Q 10.6 | Page 23

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

x2 + 4y2 − 2x = 0 

Q 11 | Page 23

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

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). 

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). 

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 \[\sqrt{2/5}\] 

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.

Q 17 | Page 23

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

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. 

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. 

 

Chapter 26: Ellipse solutions [Page 27]

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. 

Q 2 | Page 27

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

Q 3 | Page 27

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

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

Q 5 | Page 27

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

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.

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.

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. 

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. 

Chapter 26: Ellipse solutions [Pages 27 - 29]

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

Q 2 | Page 28

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

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

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

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

     
Q 6 | Page 28

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

  • \[\frac{\sqrt{3}}{2}\]

     

  • \[\frac{2}{\sqrt{3}}\]

     

  • \[\frac{1}{\sqrt{2}}\]

     

  • \[\frac{\sqrt{2}}{3}\]

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

Q 8 | Page 28

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

  • 2/5

  • 4/5

  • 1/3

  • 1/5

  • 3/5

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

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

Q 11 | Page 28

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

  • \[\frac{5}{6}\]

     

  • \[\frac{3}{5}\]

     

  • \[\frac{\sqrt{2}}{3}\]

     

  • \[\frac{\sqrt{5}}{3}\]

     

Q 12 | Page 28

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

  • \[\frac{1}{2\sqrt{3}}\]

     

  • \[\frac{1}{\sqrt{3}}\]

     

  • \[\frac{\sqrt{5}}{3}\]

     

  • \[\frac{\sqrt{5}}{6}\]

     

Q 13 | Page 28

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

  • 2/3

  •  3/4

  • 4/5

  • 1/2

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 = \[- 2\sqrt{3}\]

     

Q 15 | Page 29

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

  • \[\frac{1}{2}\]

     

  • \[\frac{1}{\sqrt{2}}\]

     

  • \[\frac{\sqrt{3}}{2}\]

     

  • \[\frac{\sqrt{3}}{4}\]

     

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

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

     

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

     

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

     

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

     

Q 17 | Page 29

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

  • 32

  • 18

  • 16

  • 8

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

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

Q 20 | Page 29

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

  • 25/16

  • 4/5

  • 16/25

  • 5/4

Q 21 | Page 29

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

  • \[\frac{1}{3}\]

     

  • \[\frac{1}{\sqrt{3}}\]

     

  • \[\frac{1}{\sqrt{2}}\]

     

  • \[\frac{2\sqrt{2}}{3}\]

     

  • \[\frac{2}{3\sqrt{2}}\]

     

Q 22 | Page 29

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

  • 3/5

  • 1/3

  •  2/5

  • 1/5

Q 23 | Page 29

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

  • 2/3

  • 3/4

  •  4/5

  • 1/2

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

RD Sharma Mathematics Class 11

Mathematics Class 11

RD Sharma solutions for Class 11 Mathematics chapter 26 - Ellipse

RD Sharma solutions for Class 11 Maths 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 Mathematics Class 11 solutions in a manner that help students grasp basic concepts better and faster.

Further, we at shaalaa.com are providing such solutions so that students can prepare for written exams. RD Sharma textbook solutions can be a core help for self-study and acts as a perfect self-help guidance for students.

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

Using RD Sharma Class 11 solutions Ellipse exercise by students are an easy way to prepare for the exams, as they involve solutions arranged chapter-wise also page wise. The questions involved in RD Sharma Solutions are important questions that can be asked in the final exam. Maximum students of CBSE Class 11 prefer RD Sharma Textbook Solutions to score more in exam.

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