#### Chapters

Chapter 2: Relations

Chapter 3: Functions

Chapter 4: Measurement of Angles

Chapter 5: Trigonometric Functions

Chapter 6: Graphs of Trigonometric Functions

Chapter 7: Values of Trigonometric function at sum or difference of angles

Chapter 8: Transformation formulae

Chapter 9: Values of Trigonometric function at multiples and submultiples of an angle

Chapter 10: Sine and cosine formulae and their applications

Chapter 11: Trigonometric equations

Chapter 12: Mathematical Induction

Chapter 13: Complex Numbers

Chapter 14: Quadratic Equations

Chapter 15: Linear Inequations

Chapter 16: Permutations

Chapter 17: Combinations

Chapter 18: Binomial Theorem

Chapter 19: Arithmetic Progression

Chapter 20: Geometric Progression

Chapter 21: Some special series

Chapter 22: Brief review of cartesian system of rectangular co-ordinates

Chapter 23: The straight lines

Chapter 24: The circle

Chapter 25: Parabola

Chapter 26: Ellipse

Chapter 27: Hyperbola

Chapter 28: Introduction to three dimensional coordinate geometry

Chapter 29: Limits

Chapter 30: Derivatives

Chapter 31: Mathematical reasoning

Chapter 32: Statistics

Chapter 33: Probability

#### RD Sharma Mathematics Class 11

## Chapter 26: Ellipse

#### Chapter 26: Ellipse solutions [Pages 22 - 23]

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

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

(i) 4*x*^{2} + 9*y*^{2} = 1

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

(ii) 5*x*^{2} + 4*y*^{2} = 1

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

(iii) 4*x*^{2} + 3*y*^{2} = 1

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

(iv) 25*x*^{2} + 16*y*^{2} = 1600.

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

(v) 9*x*^{2} + 25*y*^{2} = 225

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 \[\sqrt{\frac{2}{5}}\]

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the case:

(vi) Vertices (± 5, 0), foci (± 4, 0)

Find the equation of the ellipse in the case:

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

Find the equation of the ellipse in the following case:

Vertices (± 6, 0), foci (± 4, 0)

Find the equation of the ellipse in the following case:

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

Find the equation of the ellipse in the following case:

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

Find the equation of the ellipse in the following case:

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

Find the equation of the ellipse in the following case:

Length of minor axis 16 foci (0, ± 6)

Find the equation of the ellipse in the following case:

Foci (± 3, 0), *a* = 4

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

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.

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.

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

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

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

*x*^{2} + 2*y*^{2} − 2*x* + 12*y* + 10 = 0

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

*x*^{2} + 4*y*^{2} − 4*x* + 24*y* + 31 = 0

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

4*x*^{2} + *y*^{2} − 8*x* + 2*y* + 1 = 0

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

3*x*^{2} + 4*y*^{2} − 12*x* − 8*y* + 4 = 0

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

4*x*^{2} + 16*y*^{2} − 24*x* − 32*y* − 12 = 0

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

*x*^{2} + 4*y*^{2} − 2*x* = 0

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

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

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

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

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 \[\sqrt{2/5}\]

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

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

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.

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]

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.

Write the eccentricity of the ellipse 9*x*^{2} + 5*y*^{2} − 18*x* − 2*y* − 16 = 0.

Write the centre and eccentricity of the ellipse 3*x*^{2} + 4*y*^{2} − 6*x* + 8*y* − 5 = 0.

*PSQ* is a focal chord of the ellipse 4*x*^{2} + 9*y*^{2} = 36 such that *SP* = 4. If *S*' is the another focus, write the value of *S*'*Q*.

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

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

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.

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.

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]

For the ellipse 12x^{2} + 4y^{2} + 24x − 16y + 25 = 0

centre is (−1, 2)

lengths of the axes are \[\sqrt{3}\] and 1

eccentricity = `sqrt(2/3)`

all of these

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

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

x

^{2}^{ }+ y^{2}= a^{2}+ b^{2}x

^{2}^{ }+ y^{2}= a^{2}x

^{2}+ y^{2}= 2a^{2}x

^{2}+ y^{2}= a^{2}− b^{2}

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

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

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

- \[\frac{\sqrt{3}}{2}\]
- \[\frac{2}{\sqrt{3}}\]
- \[\frac{1}{\sqrt{2}}\]
\[\frac{\sqrt{2}}{3}\]

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

ae

2ae

ae

^{2}2ae

^{2}

The eccentricity of the conic 9x^{2} + 25y^{2} = 225 is

2/5

4/5

1/3

1/5

3/5

The latus-rectum of the conic 3x^{2} + 4y^{2} − 6x + 8y − 5 = 0 is

3

- \[\frac{\sqrt{3}}{2}\]
- \[\frac{2}{\sqrt{3}}\]
none of these

The equations of the tangents to the ellipse 9x^{2} + 16y^{2} = 144 from the point (2, 3) are

y = 3, x = 5

x = 2, y = 3

x = 3, y = 2

x + y = 5, y = 3

The eccentricity of the ellipse 4*x*^{2} + 9*y*^{2} + 8*x* + 36*y* + 4 = 0 is

- \[\frac{5}{6}\]
- \[\frac{3}{5}\]
- \[\frac{\sqrt{2}}{3}\]
- \[\frac{\sqrt{5}}{3}\]

The eccentricity of the ellipse 4x^{2} + 9y^{2} = 36 is

- \[\frac{1}{2\sqrt{3}}\]
- \[\frac{1}{\sqrt{3}}\]
- \[\frac{\sqrt{5}}{3}\]
- \[\frac{\sqrt{5}}{6}\]

The eccentricity of the ellipse 5x^{2} + 9y^{2} = 1 is

2/3

3/4

4/5

1/2

For the ellipse x^{2} + 4y^{2} = 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 = \[- 2\sqrt{3}\]

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

- \[\frac{1}{2}\]
- \[\frac{1}{\sqrt{2}}\]
- \[\frac{\sqrt{3}}{2}\]
- \[\frac{\sqrt{3}}{4}\]

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

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

The sum of the focal distances of any point on the ellipse 9x^{2} + 16y^{2} = 144 is

32

18

16

8

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

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

The eccentricity of the ellipse 9x^{2} + 25y^{2} − 18x − 100y − 116 = 0, is

25/16

4/5

16/25

5/4

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

- \[\frac{1}{3}\]
- \[\frac{1}{\sqrt{3}}\]
- \[\frac{1}{\sqrt{2}}\]
- \[\frac{2\sqrt{2}}{3}\]
- \[\frac{2}{3\sqrt{2}}\]

The eccentricity of the ellipse 25x^{2} + 16y^{2} = 400 is

3/5

1/3

2/5

1/5

The eccentricity of the ellipse 5x^{2} + 9y^{2} = 1 is

2/3

3/4

4/5

1/2

The eccentricity of the ellipse 4x^{2} + 9y^{2} = 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

#### Textbook solutions for 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.

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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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