# CBSE Solutions for Class 11 Maths

#### Select CBSE Solutions for class 10 Subject & Chapters Wise :

If the equation of a circle is 2λx2 + (4λ − 6)y2 − 8x + 12y − 2 = 0, then the coordinates of centre are _________

(2/3, −1)

The equation x2 + y2 + 2x − 4y + 5 = 0 represents _____________

a point

If the centroid of an equilateral triangle is (1, 1) and its one vertex is (2, 2), then the equation of its circumcircle is _____________

x2 + y2 − 2x − 2y = 0

The equation of the incircle formed by the coordinate axes and the line 4x + 3y = 6 is_____________

4 (x2 + y2 − x − y) + 1 = 0

the circles x2 + y2 = 9 and x2 + y2 + 8y + 2c = 0 touch each other, then c is equal to _____________

15

If the circle x2 + y2 + 2ax + 6y + 9 = 0 touches x-axis, then the value of a is _____________

± 3

The equation of a circle with radius 4 and touching both the coordinate axes is _____________

xy± 8x ± 8y + 16 = 0

The equation of the circle passing through the origin which cuts off intercept of length 6 and 6 from the axes is _____________

x2 + y2 − 6x − 7y = 3√2 - 18

The circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x-axis, if g2 _____________

c

If (x, 3) and (3, 5) are the extremities of a diameter of a circle with centre at (2, y), then the values of x and y are _____________

x = 1, y = 4

Equation of the diameter of the circle x2 + y2 + 4x - 2y = 0 which passes through the origin is _____________

x + 2y = 0

The vertex of the parabola (y + k)2 = 8k (x − k) is _____________

(k, −k)

The equation of the parabola whose vertex is (k, 0) and the directrix has the equation y = 3k, is _____________

x2 − 2xy + y2 + 6kx + 10ky – 7k2 = 0

The locus of the points of trisection of the double ordinates of a parabola is a _____________

x2 − 2xy + y2 + 6kx + 10ky – 7k2 = 0

The equation of the parabola with focus (0, 0) and directrix x + y = 7 is _____________

x2 + y2 − 2xy + 14x + 14y − 49 = 0

In the parabola y2 = 4kx, the length of the chord passing through the vertex and inclined to the axis at π/4 is _____________

4√2k

The equation 9x2 + y2 + 6xy − 74x − 78y + 212 = 0 represents _____________

a parabola

Which points lie on the parabola x2 = ay?

x = aty = at2

Which points lie on the parabola x2 = 9ay?

x = 3aty = 3at2

Which points lie on the parabola 16x2 = 16ay?

x = aty = at2

Equation of the hyperbola whose vertices are (± 5, 0) and foci at (± 13, 0), is_____________

144x2 − 25y2 = 3600

If e1 and e2 are respectively the eccentricities of the ellipse x2/18 + y2/4 = 1 and the hyperbola x2/9 - y2/4 = 1, then the relation between e1 and e2 is_____________

e12 + e22 = 3

The distance between the directrices of the hyperbola x = 8 sec θ, y = 8 tan θ, is_____________

8√2

The equation of the conic with focus at (1, −1) directrix along x − y + 1 = 0 and eccentricity √2 is_____________

2xy − 4x + 4y + 1 = 0

The eccentricity of the conic 25x2 − 144y2 = 3600 is_____________

13/12

Find the radius of each of the following circles :  x2 + y2 − 4x + 6y = 5

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
x2 + y2 − 4x + 6y = 5

The given equation can be rewritten as follows:
(x−2)2+(y+3)2−4−9=5
⇒(x−2)2 + (y+3)2 =18

Find the radius of each of the following circles :   (x + 5)2 + (y + 1)2 = 9

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
(x + 5)2 + (y + 1)2 = 9

Find the centre of each of the following circles :  x2 + y− x + 2y − 3 = 0.

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
x2 + y2− x + 2y − 3=0

The given equation can be rewritten as follows:
(x− ½ )2+(y+1)2− ¼ −1−3=0
⇒(x− ½ )2 + (y+1)2 = 17/4
Thus, the centre is ( ½ ,−1)

Find the radius of each of the following circles :  (x − 1)2 + y2 = 4

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
(x − 1)2 + y2 = 4

Find the centre of each of the following circles :  x2 + y2 − 4x + 6y = 5

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
x2 + y2 − 4x + 6y = 5

The given equation can be rewritten as follows:
(x−2)2+(y+3)2−4−9=5
⇒(x−2)2 + (y+3)2 =18

Thus, the centre is (2, −3).

Find the centre of each of the following circles :  (x + 5)2 + (y + 1)2 = 9

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
(x + 5)2 + (y + 1)2 = 9

Here, p = −5, q = −1

Thus, the centre is (-5, −1).

Find the centre of each of the following circles :  (x − 1)2 + y2 = 4

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2
Given:
(x − 1)2 + y2 = 4

Here, p = 1, q = 0 and a = 2

Thus, the centre is (1, 0)

Find the vertex of the following parabolas  :  4x2 + y = 0

Given:
4x2 + y = 0
⇒-y/4=x2

On comparing the given equation with x2=−4ay:

4a=1/4

⇒a=1/16

∴ Vertex = (0, 0)

Find the vertex of the following parabolas  :  y2 = 8x

Given:
y2 = 8x

On comparing the given equation with y2=4ax:
4a=8⇒a=2

∴ Vertex = (0, 0)

Find the radius of each of the following circles :  x2 + y− x + 2y − 3 = 0.

Let (p, q) be the centre of a circle with radius a.
Thus, its equation will be (x−p)2 + (y−q)2 = a2

Given:
x2 + y2− x + 2y − 3=0

The given equation can be rewritten as follows:
(x− ½ )2+(y+1)2− ¼ −1−3=0
⇒(x− ½ )2 + (y+1)2 = 17/4

Thus, the centre is ( ½ ,−1) and and the radius is √17/2.