# NCERT Solutions for Class 11 Maths Maths Chapter 11

## Conic Sections Class 11

### Exercise 11.1 : Solutions of Questions on Page Number : 241

Q1 :

Find the equation of the circle with centre (0, 2) and radius 2

The equation of a circle with centre (h, k) and radius r is given as

( - h)2 + (y ­- k)2 = r2

It is given that centre (h, k) = (0, 2) and radius (r) = 2.

Therefore, the equation of the circle is

(x - 0)2 + (y - 2)2 = 22

x2 + y2 + 4 ­- 4 y = 4

x2 + y2 ­- 4y = 0

Q2 :

Find the equation of the circle with centre (-2, 3) and radius 4

The equation of a circle with centre (h, k) and radius r is given as

( - h)2 + (y ­- k)2 = r2

It is given that centre (h, k) = (-2, 3) and radius (r) = 4.

Therefore, the equation of the circle is

(x + 2)2 + (y - 3)2 = (4)2

x2 + 4x + 4 + y2 - 6y + 9 = 16

x2 + y2 + 4x - 6y - 3 = 0

Q3 :

Find the equation of the circle with centreand radius

Q4 :

Find the equation of the circle with centre (1, 1) and radius

Q5 :

Find the equation of the circle with centre (â€“a, â€“b) and radius

Q6 :

Find the centre and radius of the circle (x + 5)2 + (y - 3)2 = 36

Q7 :

Find the centre and radius of the circle x2 + y2 - 4x - 8y - 45 = 0

Q8 :

Find the centre and radius of the circle x2 + y2 - 8x + 10y - 12 = 0

Q9 :

Find the centre and radius of the circle 2x2 + 2y2 - x = 0

Q10 :

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.

Q11 :

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.

Q12 :

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

Q13 :

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

Q14 :

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

Q15 :

Does the point (-2.5, 3.5) lie inside, outside or on the circle x2 + y2 = 25?

### Exercise 11.2 : Solutions of Questions on Page Number : 246

Q1 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 12x

Q2 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = 6y

Q3 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = - 8x

Q4 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = - 16y

Q5 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for y2 = 10x

Q6 :

Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x2 = -9y

Q7 :

Find the equation of the parabola that satisfies the following conditions: Focus (6, 0); directrix x = -6

Q8 :

Find the equation of the parabola that satisfies the following conditions: Focus (0, -3); directrix y = 3

Q9 :

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0); focus (3, 0)

Q10 :

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) focus (-2, 0)

Q11 :

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0) passing through (2, 3) and axis is along x-axis

Q12 :

Find the equation of the parabola that satisfies the following conditions: Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis

### Exercise 11.3 : Solutions of Questions on Page Number : 255

Q1 :

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

Q2 :

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

Q3 :

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

Q4 :

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

Q5 :

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

Q6 :

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

Q7 :

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 36x2 + 4y2 = 144

Q8 :

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 16x2 + y2 = 16

Q9 :

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 4x2 + 9y2 = 36

Q10 :

Find the equation for the ellipse that satisfies the given conditions: Vertices (±5, 0), foci (±4, 0)

Q11 :

Find the equation for the ellipse that satisfies the given conditions: Vertices (0, ±13), foci (0, ±5)

Q12 :

Find the equation for the ellipse that satisfies the given conditions: Vertices (±6, 0), foci (±4, 0)

Q13 :

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis (±3, 0), ends of minor axis (0, ±2)

Q14 :

Find the equation for the ellipse that satisfies the given conditions: Ends of major axis, ends of minor axis ( ±1, 0)

Q15 :

Find the equation for the ellipse that satisfies the given conditions: Length of major axis 26, foci (±5, 0)

Q16 :

Find the equation for the ellipse that satisfies the given conditions: Length of minor axis 16, foci (0, ±6)

Q17 :

Find the equation for the ellipse that satisfies the given conditions: Foci (±3, 0), a = 4

Q18 :

Find the equation for the ellipse that satisfies the given conditions: b = 3, c = 4, centre at the origin; foci on the x axis.

Q19 :

Find the equation for the ellipse that satisfies the given conditions: Centre at (0, 0), major axis on the y-axis and passes through the points (3, 2) and (1, 6).

Q20 :

Find the equation for the ellipse that satisfies the given conditions: Major axis on the x-axis and passes through the points (4, 3) and (6, 2).

### Exercise 11.4 : Solutions of Questions on Page Number : 262

Q1 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

Q2 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola

Q3 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 9y2 - 4x2 = 36

Q4 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 16x2 - 9y2 = 576

Q5 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 5y2 - 9x2 = 36

Q6 :

Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola 49y2 - 16x2 = 784

Q7 :

Find the equation of the hyperbola satisfying the give conditions: Vertices (±2, 0), foci (±3, 0)

Q8 :

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±5), foci (0, ±8)

Q9 :

Find the equation of the hyperbola satisfying the give conditions: Vertices (0, ±3), foci (0, ±5)

Q10 :

Find the equation of the hyperbola satisfying the give conditions: Foci (±5, 0), the transverse axis is of length 8.

Q11 :

Find the equation of the hyperbola satisfying the give conditions: Foci (0, ±13), the conjugate axis is of length 24.

Q12 :

Find the equation of the hyperbola satisfying the give conditions: Foci, the latus rectum is of length 8.

Q13 :

Find the equation of the hyperbola satisfying the give conditions: Foci (±4, 0), the latus rectum is of length 12

Q14 :

Find the equation of the hyperbola satisfying the give conditions: Vertices ( ±7, 0),

Q15 :

Find the equation of the hyperbola satisfying the give conditions: Foci, passing through (2, 3)

### Exercise Miscellaneous : Solutions of Questions on Page Number : 264

Q1 :

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

Q2 :

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

Q3 :

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?

Q4 :

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.

Q5 :

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.

Q6 :

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.

Q7 :

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.

Q8 :

A man running a racecourse notes that the sum of the distances from the two flag posts form 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.

Q9 :

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.