Class 11 Maths NCERT Solutions For Chapter 11 Conic Sections

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

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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