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# RD Sharma solutions for Class 11 Mathematics chapter 25 - Parabola

## Chapter 25: Parabola

Ex. 25.10Ex. 25.20Others

#### Chapter 25: Parabola Exercise 25.10 solutions [Pages 24 - 25]

Ex. 25.10 | Q 1.1 | Page 24

Find the equation of the parabola whose:

focus is (3, 0) and the directrix is 3x + 4y = 1

Ex. 25.10 | Q 1.2 | Page 24

Find the equation of the parabola whose:

focus is (1, 1) and the directrix is x + y + 1 = 0

Ex. 25.10 | Q 1.3 | Page 24

Find the equation of the parabola whose:

focus is (0, 0) and the directrix 2x − y − 1 = 0

Ex. 25.10 | Q 1.4 | Page 24

Find the equation of the parabola whose:

focus is (2, 3) and the directrix x − 4y + 3 = 0.

Ex. 25.10 | Q 2 | Page 24

Find the equation of the parabola whose focus is the point (2, 3) and directrix is the line x − 4y + 3 = 0. Also, find the length of its latus-rectum.

Ex. 25.10 | Q 3.1 | Page 24

Find the equation of the parabola if

the focus is at (−6, −6) and the vertex is at (−2, 2)

Ex. 25.10 | Q 3.2 | Page 24

Find the equation of the parabola if

the focus is at (0, −3) and the vertex is at (0, 0)

Ex. 25.10 | Q 3.3 | Page 24

Find the equation of the parabola if the focus is at (0, −3) and the vertex is at (−1, −3)

Ex. 25.10 | Q 3.4 | Page 24

Find the equation of the parabola if the focus is at (a, 0) and the vertex is at (a', 0)

Ex. 25.10 | Q 3.5 | Page 24

Find the equation of the parabola if  the focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x − y = 3.

Ex. 25.10 | Q 4.1 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola y2 = 8

Ex. 25.10 | Q 4.2 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

4x2 + y = 0

Ex. 25.10 | Q 4.3 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas

y2 − 4y − 3x + 1 = 0

Ex. 25.10 | Q 4.4 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y2 − 4y + 4x = 0

Ex. 25.10 | Q 4.5 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y2 + 4x + 4y − 3 = 0

Ex. 25.10 | Q 4.6 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y2 = 8x + 8

Ex. 25.10 | Q 4.7 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

4 (y − 1)2 = − 7 (x − 3)

Ex. 25.10 | Q 4.8 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

y2 = 5x − 4y − 9

Ex. 25.10 | Q 4.9 | Page 24

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola

x2 + y = 6x − 14

Ex. 25.10 | Q 5 | Page 24

For the parabola y2 = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines from the vertex to its extremities are at right angles.

Ex. 25.10 | Q 6 | Page 25

Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2 = 12y$  to the ends of its latus rectum.

Ex. 25.10 | Q 7 | Page 25

Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x − 4y = 2. Find also the length of the latus-rectum.

Ex. 25.10 | Q 8 | Page 25

At what point of the parabola x2 = 9y is the abscissa three times that of ordinate?

Ex. 25.10 | Q 9 | Page 25

Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).

Ex. 25.10 | Q 10 | Page 25

Find the equation of a parabola with vertex at the origin and the directrix, y = 2.

Ex. 25.10 | Q 11 | Page 25

Find the equation of the parabola whose focus is (5, 2) and having vertex at (3, 2).

Ex. 25.10 | Q 12 | Page 25

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest wire being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

Ex. 25.10 | Q 13 | Page 25

Find the equations of the lines joining the vertex of the parabola y2 = 6x to the point on it which have abscissa 24.

Ex. 25.10 | Q 14 | Page 25

Find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.

Ex. 25.10 | Q 15 | Page 25

Find the length of the line segment joining the vertex of the parabola y2 = 4ax and a point on the parabola where the line-segment makes an angle θ to the x-axis.

Ex. 25.10 | Q 16 | Page 25

If the points (0, 4) and (0, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

Ex. 25.10 | Q 17 | Page 25

If the line y = mx + 1 is tangent to the parabola y2 = 4x, then find the value of m

#### Chapter 25: Parabola Exercise 25.20 solutions [Page 28]

Ex. 25.20 | Q 1 | Page 28

Write the axis of symmetry of the parabola y2 = x

Ex. 25.20 | Q 2 | Page 28

Write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0.

Ex. 25.20 | Q 3 | Page 28

Write the equation of the directrix of the parabola x2 − 4x − 8y + 12 = 0.

Ex. 25.20 | Q 4 | Page 28

Write the equation of the parabola with focus (0, 0) and directrix x + y − 4 = 0.

Ex. 25.20 | Q 5 | Page 28

Write the length of the chord of the parabola y2 = 4ax which passes through the vertex and is inclined to the axis at $\frac{\pi}{4}$

Ex. 25.20 | Q 6 | Page 28

If b and c are lengths of the segments of any focal chord of the parabola y2 = 4ax, then write the length of its latus-rectum.

Ex. 25.20 | Q 7 | Page 28

PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ

Ex. 25.20 | Q 8 | Page 28

Write the coordinates of the vertex of the parabola whose focus is at (−2, 1) and directrix is the line x + y − 3 = 0.

Ex. 25.20 | Q 9 | Page 28

If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix.

Ex. 25.20 | Q 10 | Page 28

If the parabola y2 = 4ax passes through the point (3, 2), then find the length of its latus rectum.

Ex. 25.20 | Q 11 | Page 28

Write the equation of the parabola whose vertex is at (−3,0) and the directrix is x + 5 = 0.

#### Chapter 25: Parabola solutions [Pages 28 - 30]

Q 1 | Page 29

The coordinates of the focus of the parabola y2 − x − 2y + 2 = 0 are

•  (5/4, 1)

• (1/4, 0)

• (1, 1)

•  none of these

Q 2 | Page 29

The vertex of the parabola (y + a)2 = 8a (x − a) is

• (−a, −a)

•  (a, −a)

•  (−aa

•  none of these

Q 3 | Page 29

If the focus of a parabola is (−2, 1) and the directrix has the equation x + y = 3, then its vertex is

• (0, 3)

• (−1, 1/2)

• (−1, 2)

• (2, −1)

Q 4 | Page 29

The equation of the parabola whose vertex is (a, 0) and the directrix has the equation y = 3a, is

• x2 + y2 + 2xy + 6ax + 10ay + 7a2 = 0

• x2 − 2xy + y2 + 6ax + 10ay − 7a2 = 0

• x2 − 2xy + y2 − 6ax + 10ay − 7a2 = 0

• none of these

Q 5 | Page 29

The parametric equations of a parabola are x = t2 + 1, y = 2t + 1. The cartesian equation of its directrix is

• x = 0

• x + 1 = 0

• y = 0

•  none of these

Q 6 | Page 29

If the coordinates of the vertex and the focus of a parabola are (−1, 1) and (2, 3) respectively, then the equation of its directrix is

•  3x + 2y + 14 = 0

• 3x + 2y − 25 = 0

• 2x − 3y + 10 = 0

•  none of these.

Q 7 | Page 29

The locus of the points of trisection of the double ordinates of a parabola is a

• pair of lines

•  circle

• parabola

• straight line

Q 8 | Page 29

The equation of the directrix of the parabola whose vertex and focus are (1, 4) and (2, 6) respectively is

• x + 2y = 4

• x − y = 3 1

•  2x + y = 5

• x + 3y = 8

Q 9 | Page 29

If V and S are respectively the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0, then SV

• 1/2

• none of these

Q 10 | Page 29

The directrix of the parabola x2 − 4x − 8y + 12 = 0 is

• y = 0

• x = 1

•  y = − 1

• x = − 1

Q 11 | Page 29

The equation of the parabola with focus (0, 0) and directrix x + y = 4 is

• x2 + y2 − 2xy + 8x + 8y − 16 = 0

•  x2 + y2 − 2xy + 8x + 8y = 0

• x2 + y2 + 8x + 8y − 16 = 0

•  x2 − y2 + 8x + 8y − 16 = 0

Q 12 | Page 29

The line 2x − y + 4 = 0 cuts the parabola y2 = 8x in P and Q. The mid-point of PQ is

•  (1, 2)

•  (1, −2)

•  (−1, 2)

•  (−1, −2)

Q 13 | Page 28

In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is

• $4\sqrt{2}a$

• $2\sqrt{2}a$

• $\sqrt{2}a$

• none of these

Q 14 | Page 29

The equation 16x2 + y2 + 8xy − 74x − 78y + 212 = 0 represents

• a circle

• a parabola

•  an ellipse

•  a hyperbola

Q 15 | Page 30

The length of the latus-rectum of the parabola y2 + 8x − 2y + 17 = 0 is

•  4

•  8

• 16

Q 16 | Page 30

The vertex of the parabola x2 + 8x + 12y + 4 = 0 is

• (−4, 1)

• (4, −1)

•  (−4, −1)

• (4, 1)

Q 17 | Page 30

The vertex of the parabola (y − 2)2 = 16 (x − 1) is

• (1, 2)

•  (−1, 2)

•  (1, −2)

• (2, 1)

Q 18 | Page 30

The length of the latus-rectum of the parabola 4y2 + 2x − 20y + 17 = 0 is

•  3

•  1/2

Q 19 | Page 30

The length of the latus-rectum of the parabola x2 − 4x − 8y + 12 = 0 is

•  6

• 10

Q 20 | Page 30

The focus of the parabola y = 2x2 + x is

• (0, 0)

•  (1/2, 1/4)

•  (−1/4, 0)

• (−1/4, 1/8)

Q 21 | Page 30

Which of the following points lie on the parabola x2 = 4ay

• x = at2y = 2at

• x = 2aty = at

• x = 2at2y = at

• x = 2aty = at

Q 22 | Page 30

The equation of the parabola whose focus is (1, −1) and the directrix is x + y + 7 = 0 is

•  x2 + y2 − 2xy − 18x − 10y = 0

•  x2 − 18x − 10y − 45 = 0

•  x2 + y2 − 18x − 10y − 45 = 0

•  x2 + y2 − 2xy − 18x − 10y − 45 = 0

## Chapter 25: Parabola

Ex. 25.10Ex. 25.20Others

## RD Sharma solutions for Class 11 Mathematics chapter 25 - Parabola

RD Sharma solutions for Class 11 Maths chapter 25 (Parabola) 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 25 Parabola 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 Parabola 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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