#### 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

## Chapter 25: Parabola

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 25 ParabolaExercise 25.1 [Pages 24 - 25]

Find the equation of the parabola whose:

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

Find the equation of the parabola whose:

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

Find the equation of the parabola whose:

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

Find the equation of the parabola whose:

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

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

Find the equation of the parabola if

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

Find the equation of the parabola if

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

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

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

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.

Find the vertex, focus, axis, directrix and latus-rectum of the following parabola *y*^{2} = 8*x *

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

4*x*^{2} + *y* = 0

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

*y*^{2} − 4*y** *− 3*x* + 1 = 0

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

*y*^{2} − 4*y* + 4*x* = 0

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

*y*^{2} + 4*x* + 4*y* − 3 = 0

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

*y*^{2} = 8*x* + 8*y *

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

4 (*y* − 1)^{2} = − 7 (*x* − 3)

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

*y*^{2} = 5*x* − 4*y* − 9

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

*x*^{2} + *y* = 6*x* − 14

For the parabola *y*^{2} = 4*px* 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.

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.

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 3*x* − 4*y* = 2. Find also the length of the latus-rectum.

At what point of the parabola *x*^{2} = 9*y* is the abscissa three times that of ordinate?

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

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

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

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.

Find the equations of the lines joining the vertex of the parabola *y*^{2} = 6*x* to the point on it which have abscissa 24.

Find the coordinates of points on the parabola *y*^{2} = 8*x* whose focal distance is 4.

Find the length of the line segment joining the vertex of the parabola* y*^{2} = 4*ax* and a point on the parabola where the line-segment makes an angle θ to the *x*-axis.

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

If the line *y* = *mx* + 1 is tangent to the parabola *y*^{2} = 4*x,* then find the value of *m*.

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 25 ParabolaExercise 25.2 [Page 28]

Write the axis of symmetry of the parabola *y*^{2} = *x*.

Write the distance between the vertex and focus of the parabola *y*^{2} + 6*y* + 2*x* + 5 = 0.

Write the equation of the directrix of the parabola *x*^{2} − 4*x* − 8*y* + 12 = 0.

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

Write the length of the chord of the parabola *y*^{2} = 4*ax* which passes through the vertex and is inclined to the axis at \[\frac{\pi}{4}\]

If *b* and *c* are lengths of the segments of any focal chord of the parabola *y*^{2} = 4*ax*, then write the length of its latus-rectum.

*PSQ* is a focal chord of the parabola *y*^{2} = 8*x*. If *SP* = 6, then write *SQ*.

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

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.

If the parabola *y*^{2} = 4*ax* passes through the point (3, 2), then find the length of its latus rectum.

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

#### RD Sharma solutions for Class 11 Mathematics Textbook Chapter 25 Parabola [Pages 28 - 30]

The coordinates of the focus of the parabola *y*^{2} − *x* − 2*y* + 2 = 0 are

(5/4, 1)

(1/4, 0)

(1, 1)

none of these

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

(−

*a*, −*a*)(

*a*, −*a*)(−

*a*,*a*)none of these

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)

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

*x*^{2}+*y*^{2}+ 2*xy*+ 6*ax*+ 10*ay*+ 7*a*^{2}= 0*x*^{2}− 2*xy*+*y*^{2}+ 6*ax*+ 10*ay*− 7*a*^{2}= 0*x*^{2}− 2*xy*+*y*^{2}− 6*ax*+ 10*ay*− 7*a*^{2}= 0none of these

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

*x*= 0*x*+ 1 = 0*y*= 0none of these

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

3

*x*+ 2*y*+ 14 = 03

*x*+ 2*y*− 25 = 02

*x*− 3*y*+ 10 = 0none of these.

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

pair of lines

circle

parabola

straight line

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

*x*+ 2*y*= 4*x*−*y*= 3 12

*x*+*y*= 5*x*+ 3*y*= 8

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

2

1/2

1

none of these

The directrix of the parabola *x*^{2} − 4*x* − 8*y* + 12 = 0 is

*y*= 0*x*= 1*y*= − 1*x*= − 1

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

*x*^{2}+*y*^{2}− 2*xy**x*+ 8*y*− 16 = 0*x*^{2}+*y*^{2}− 2*xy*+ 8*x*+ 8*y*= 0*x*^{2}+*y*^{2}+ 8*x*+ 8*y*− 16 = 0*x*^{2}−*y*^{2}+ 8*x*+ 8*y*− 16 = 0

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

(1, 2)

(1, −2)

(−1, 2)

(−1, −2)

In the parabola *y*^{2} = 4*ax*, 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

The equation 16*x*^{2} + *y*^{2} + 8*xy** *− 74*x* − 78*y* + 212 = 0 represents

a circle

a parabola

an ellipse

a hyperbola

The length of the latus-rectum of the parabola *y*^{2} + 8*x* − 2*y* + 17 = 0 is

2

4

8

16

The vertex of the parabola *x*^{2} + 8*x* + 12*y* + 4 = 0 is

(−4, 1)

(4, −1)

(−4, −1)

(4, 1)

The vertex of the parabola (*y* − 2)^{2} = 16 (*x* − 1) is

(1, 2)

(−1, 2)

(1, −2)

(2, 1)

The length of the latus-rectum of the parabola 4*y*^{2} + 2*x* − 20*y* + 17 = 0 is

3

6

1/2

9

The length of the latus-rectum of the parabola *x*^{2}^{ }− 4*x* − 8*y* + 12 = 0 is

4

6

8

10

The focus of the parabola *y* = 2*x*^{2} + *x* is

(0, 0)

(1/2, 1/4)

(−1/4, 0)

(−1/4, 1/8)

Which of the following points lie on the parabola *x*^{2} = 4*ay*?

*x*=*at*^{2},*y*= 2*at**x*= 2*at*,*y*=*at*^{2 }*x*= 2*at*^{2},*y*=*at**x*= 2*at*,*y*=*at*^{2 }

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

*x*^{2}+*y*^{2}− 2*xy*− 18*x*− 10*y*= 0*x*^{2}− 18*x*− 10*y*− 45 = 0*x*^{2}+*y*^{2}− 18*x*− 10*y*− 45 = 0*x*^{2}+*y*^{2}− 2*xy*− 18*x*− 10*y*− 45 = 0

## Chapter 25: Parabola

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

RD Sharma solutions for Class 11 Mathematics Textbook 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 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 25 Parabola 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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