# Class 11 Maths NCERT Solutions For Chapter 11 Conic Sections

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## 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 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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