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Chapters
2: Relations
3: Functions
4: Measurement of Angles
5: Trigonometric Functions
6: Graphs of Trigonometric Functions
7: Values of Trigonometric function at sum or difference of angles
8: Transformation formulae
9: Values of Trigonometric function at multiples and submultiples of an angle
10: Sine and cosine formulae and their applications
11: Trigonometric equations
12: Mathematical Induction
13: Complex Numbers
14: Quadratic Equations
15: Linear Inequations
16: Permutations
17: Combinations
18: Binomial Theorem
19: Arithmetic Progression
20: Geometric Progression
21: Some special series
22: Brief review of cartesian system of rectangular co-ordinates
23: The straight lines
24: The circle
▶ 25: Parabola
26: Ellipse
27: Hyperbola
28: Introduction to three dimensional coordinate geometry
29: Limits
30: Derivatives
31: Mathematical reasoning
32: Statistics
33: Probability
![RD Sharma solutions for Mathematics [English] Class 11 chapter 25 - Parabola - Shaalaa.com](/images/mathematics-english-class-11_6:972cafaba17f4949992ada196fa0f041.jpg "RD Sharma solutions for Mathematics [English] Class 11 chapter 25 - Parabola")
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Solutions for Chapter 25: Parabola
Below listed, you can find solutions for Chapter 25 of CBSE, Karnataka Board PUC RD Sharma for Mathematics [English] Class 11.
RD Sharma solutions for Mathematics [English] Class 11 25 Parabola Exercise 25.1 [Pages 24 - 25]
Find the equation of the parabola whose:
focus is (3, 0) and the directrix is 3x + 4y = 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 2x − 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 − 4y + 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:
y2 = 8x
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
4x2 + y = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas
y2 − 4y − 3x + 1 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 − 4y + 4x = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 + 4x + 4y − 3 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 8x + 8y
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
y2 = 5x − 4y − 9
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
x2 + y = 6x − 14
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.
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 3x − 4y = 2. Find also the length of the latus-rectum.
At what point of the parabola x2 = 9y 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 y2 = 6x to the point on it which have abscissa 24.
Find the coordinates of points on the parabola y2 = 8x whose focal distance is 4.
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.
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 y2 = 4x, then find the value of m.
RD Sharma solutions for Mathematics [English] Class 11 25 Parabola Exercise 25.2 [Page 28]
Write the axis of symmetry of the parabola y2 = x.
Write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0.
Write the equation of the directrix of the parabola x2 − 4x − 8y + 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 y2 = 4ax 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 y2 = 4ax, then write the length of its latus-rectum.
PSQ is a focal chord of the parabola y2 = 8x. 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 y2 = 4ax 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 Mathematics [English] Class 11 25 Parabola Exercise 25.3 [Pages 29 - 30]
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
The vertex of the parabola (y + a)2 = 8a (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 = 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
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
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.
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 + 2y = 4
x − y = 3 1
2x + y = 5
x + 3y = 8
If V and S are respectively the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0, then SV =
2
1/2
1
none of these
The directrix of the parabola x2 − 4x − 8y + 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
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
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)
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
The equation 16x2 + y2 + 8xy − 74x − 78y + 212 = 0 represents
a circle
a parabola
an ellipse
a hyperbola
The length of the latus-rectum of the parabola y2 + 8x − 2y + 17 = 0 is
2
4
8
16
The vertex of the parabola x2 + 8x + 12y + 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 4y2 + 2x − 20y + 17 = 0 is
3
6
1/2
9
The length of the latus-rectum of the parabola x2 − 4x − 8y + 12 = 0 is
4
6
8
10
The focus of the parabola y = 2x2 + x is
(0, 0)
(1/2, 1/4)
(−1/4, 0)
(−1/4, 1/8)
Which of the following points lie on the parabola x2 = 4ay?
x = at2, y = 2at
x = 2at, y = at2
x = 2at2, y = at
x = 2at, y = at2
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
Solutions for 25: Parabola
RD Sharma solutions for Mathematics [English] Class 11 chapter 25 - Parabola
Shaalaa.com has the CBSE, Karnataka Board PUC Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. RD Sharma solutions for Mathematics Mathematics [English] Class 11 CBSE, Karnataka Board PUC 25 (Parabola) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.
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Concepts covered in Mathematics [English] Class 11 chapter 25 Parabola are Sections of a Cone, Latus Rectum, 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, Parabola and its types, Latus Rectum, Eccentricity, Latus Rectum, Standard Equation of a Circle, Hyperbola and its Types, Ellipse and its Types, Eccentricity.
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