NCERT Solutions Class 11 Mathematics Chapter 11 Conic Sections Download In Pdf

Chapter 11 Conic Sections Download in pdf

>## Chapter 11 Conic Sections

## Download NCERT Solutions for Class 11 Mathematics

## (Link of Pdf file is given below at the end of the Questions List)

## In this pdf file you can see answers of following Questions

### EXERCISE 11.1

####

EXERCISE 11.2

EXERCISE 11.3

EXERCISE 11.4

####

Miscellaneous Exercise on Chapter 11

**In each of the following Exercises 1 to 5, find the equation of the circle with**

**Question 1.**centre (0,2) and radius2.

**Question 2.**centre (–2,3) and radius 4

**Question 3.**centre (
4
, 1
2
1 ) and radius
12
1

**Question 4.**centre (1,1) and radius 2

**Question 5.**centre (–a, –b) and radius a2 − b 2.In each of the following Exercises 6 to 9, find the centre and radius of the circles.

**Question 6.**(x + 5)2 + (y – 3)2 = 36

**Question 7.**x2 + y2 – 4x – 8y – 45 = 0

**Question 8.**x2 + y2 – 8x + 10y – 12 = 0

**Question 9.**2x2 + 2y2 – x = 0

**Question 10.**Find the equation of the circle passing through the points (4,1) and (6,5) and
whose centre is on the line 4x + y = 16.

**Question 11.**Find the equation of the circle passing through the points (2,3) and (–1,1) and
whose centre is on the line x – 3y – 11 = 0.

**Question 12.**Find the equation of the circle with radius 5 whose centre lies on x-axis and
passes through the point (2,3).

**Question 13.**Find the equation of the circle passing through (0,0) and making intercepts a and
b on the coordinate axes.

**Question 14.**Find the equation of a circle with centre (2,2) and passes through the point (4,5).

**Question1 5.**Does the point (–2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?

EXERCISE 11.2

**In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the
parabola, the equation of the directrix and the length of the latus rectum.
**

**Question 1.**y2 = 12x

**Question 2.**x2 = 6y

**Question 3.**y2 = – 8x

**Question 4.**x2 = – 16y

**Question 5.**y2 = 10x

**Question 6.**x2 = – 9y
In each of the Exercises 7 to 12, find the equation of the parabola that satisfies the
given conditions:

**Question 7.**Focus (6,0); directrix x = – 6

**Question 8.**Focus (0,–3); directrix y = 3

**Question 9.**Vertex (0,0); focus (3,0)

**Question 10.**Vertex (0,0); focus (–2,0
)

**Question 1.**Vertex (0,0) passing through (2,3) and axis is along x-axis.

**Question 2.**Vertex (0,0), passing through (5,2) and symmetric with respect to y-axis.

EXERCISE 11.3

In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length
of major axis, the minor axis, the eccentricity and the length of the latus rectum of the
ellipse.

**Question 1. **2 2
1
36 16
x + y =

**Question 2. **2 2
1
4 25
x + y =

**Question 3. **2 2
1
16 9
x + y =

**Question 4.** 2 2
1
25 100
x + y =

**Question 5.** 2 2
1
49 36
x + y =

**Question 6. **100 400
x2 y2 + = 1

**Question 7. **36x2 + 4y2 = 144

**Question 8. **16x2 + y2 = 16

**Question 9. **4x2 + 9y2 = 36
In each of the following Exercises 10 to 20, find the equation for the ellipse that satisfies
the given conditions:

**Question 10.** Vertices (± 5, 0), foci (± 4, 0)

**Question 11.** Vertices (0, ± 13), foci (0, ± 5)

**Question 12.**Vertices (± 6, 0), foci (± 4, 0)

**Question 13.**Ends of major axis (± 3, 0), ends of minor axis (0, ± 2)

**Question 14.**Ends of major axis (0, ± 5 ), ends of minor axis (± 1, 0)

**Question 15.**Length of major axis 26, foci (± 5, 0)

**Question 16.**Length of minor axis 16, foci (0, ± 6).

**Question 17.** Foci (± 3, 0), a = 4

**Question 18.**b = 3, c = 4, centre at the origin; foci on a x axis.

**Question 19.**Centre at (0,0), major axis on the y-axis and passes through the points (3, 2) and
(1,6).

**Question 20.** Major axis on the x-axis and passes through the points (4,3) and (6,2).

EXERCISE 11.4

**In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, the
eccentricity and the length of the latus rectum of the hyperbolas. **

**Question 1. **2 2
1
16 9
x – y =

**Question
2. **2 2
1
9 27
y – x =

**Question 3.** 9y2 – 4x2 = 36

**Question 4.** 16x2 – 9y2 = 576

**Question 5. **5y2 – 9x2 = 36

**Question 6 .**49y2 – 16x2 = 78 4 .In each of the Exercises 7 to 15, find the equations of the hyperbola satisfying the given
conditions.

**
Question 7.**Vertices (± 2, 0), foci (± 3, 0)

**Question 8.** Vertices (0, ± 5), foci (0, ± 8)

**Question 9.** Vertices (0, ± 3), foci (0, ± 5)

**Question 10.** Foci (± 5, 0), the transverse axis is of length 8.

**Question 11.**Foci (0, ±13), the conjugate axis is of length 2
4.

**Question 2.**Foci (± 3 5 , 0), the latus rectum is of length 8.

**Question 3.**Foci (± 4, 0), the latus rectum is of length 12.

**Question 4.**vertices (± 7,0), e =
3
4.

**Question 5.**Foci (0, ± 10 ), passing through (2,3)

Miscellaneous Exercise on Chapter 11

**Question 1.**If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

**Question 2.**An arch is in the form of a parabola with its axis vertical. The arch is 10 m high
and 5 m wide at the base. How wide is it 2 m from the vertex of the parabola?

**Question 3.**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 being 6 m.
Find the length of a supporting wire attached to the roadway 18 m from the
middle.

**Question 4.**An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre.
Find the height of the arch at a point 1.5 m from one end.

**
Question 5.**A rod of length 12 cm 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 the x-axis.

**Question 6.**Find the area of the triangle formed by the lines joining the vertex of the parabola
x2 = 12y to the ends of its latus rectum.

**Question 7.**A man running a racecourse notes that the sum of the distances from the two flag
posts from him is always 10 m and the distance between the flag posts is 8 m.
Find the equation of the posts traced by the man.

**Question 8.**An equilateral triangle is inscribed in the parabola y2 = 4 ax, where one vertex is
at the vertex of the parabola. Find the length of the side of the triangle.

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- Chapter 1 Sets
- chapter 2 Relations And Functions
- Chapter 3 Trigonometric Functions
- Chapter 4 Principle of Mathematical Induction
- Chapter 5 Complex Numbers and Quadratic Equations
- Chapter 6 Linear Inequalities
- Chapter 7 Permutations And Combinations
- Chapter 8 Binomial Theorem
- Chapter 9 Sequences And Series
- Chapter 10 Straight Lines
- Chapter 11 Conic Sections
- Chapter 12 Introduction To Three Dimensional Geometry
- Chapter 13 Limits and Derivatives
- Chapter 14 Mathematical Reasoning
- Chapter 15 Statistics
- Chapter 16 Probability

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