KC Sinha Mathematics Solution Class 11 Chapter 22 Conic Section: Circle Exercise 22.1

 Exercise 22.1 

Page no 22.15

Type 1

Question 1

Find the equation of the circles with :

(i) Centre $(-3,2)$ and radius 5 .

(ii) Centre $(-3,-2)$ and radius $7 .$

(iii) Centre $(a, a)$ and radius $a \sqrt{2}$.

(iv) Centre $(1,-5)$ and radius 7 .

(v) Centre $(0,0)$ and radius $4 .$

(vi) Centre $(1,1)$ and radius $\sqrt{2}$.

(vii) Centre $(-2,3)$ and radius 4 .

(viii) Centre $(0,2)$ and radius $2 .$

(ix) Centre $\left(\frac{1}{2}, \frac{1}{4}\right)$ and radius $\frac{1}{12}$.

(x) Centre $(-3,2)$ and radius 4 .

(ai) Centre $(-a,-b)$ and radius $\sqrt{a^{2}-b^{2}}$.

(xii) Centre $(a \cos \alpha, a \sin \alpha)$ and radius $a$.

(xiii) Centre $(-1,-2)$ and diameter 25 .

Question 2

Find the equation of the circle passing through $(0,0)$ and cutting intercepts $a$ and $b$ on the positive side of $x$ and $y$ axes respectively.

Question 3

Find the equation of the circle passing through the origin and cutting intercepts 10 and 24 from the positive side of $x$ and $y$ axes respectively.

Question 4

Find the equation of the circle touching :

(i) $x$-axis and having center at $(4,3)$

(ii) $x$-axis at the origin and having radius 10 .

Question 5

Find the equation of the circle having radius 5 and passing through two points On $x$-axis at distances 4 from the origin .

Question 6

Find the equation of the circle with center $(2,2)$ and passing through the point $(4,5)$

Question 7

Find the equation of image of the circle $(x-1)^{2}+(y+2)^{2}=5^{2}$ in the $x$-axis.

Question 8

Find the equation of the circle passing through the point $(2,4)$ and center at the point of intersection of the lines $x-y=4$ and $2 x+3 y=-7$.

Page no 22.16

Question 9

If the equation of two diameters of a circle are $2 x+y=6$ and $3 x+2 y=4$ and the radius is 10 , find the equation of the circle.

Question 10

Find the equation to the circle which passes through the point of intersection of $3 x-2 y-1=0$ and $4 x+y-27=0$ and whose center is $(2,3)$.

Question 11

Find the equation of the circle whose center is $(2,-3)$ and which passes through the point of intersection of $3 x+2 y=11$ and $2 x+3 y=4$.

Question 12

Find the equation of the circle passing through the center of the circle $x^{2}+y^{2}-4 x-6 y=8$ and being concentric with the circle $x^{2}+y^{2}-2 x-8 y=5$

Question 13

Find the equation of the circle passing through the point of intersection of $x+3 y=0$ and $2 x-7 y=0$ and whose center is the point of intersection of lines $x+y+1=0$ and $x-2 y+4=0$.

Question 14

Find the equation of the circle whose center is $(1,-3)$ and which touches the line $2 x-y-4=0$.

Question 15

Find the equation of the circle of radius 5 whose center lies on $y$-axis and passes through the point $(3,2)$.

Question 16

Find the equation of the circle whose radius is 5 and the center lies on the positive side of $x$-axis at a distance 5 from the origin.

Question 17

Find the equation of the circle which passes through the points $(-1,2)$ and $(3,-2)$ and whose center lies on the line $x-2 y=0$

Question 18

Find the equation of the circle passing through the points $(2,3)$ and $(-1,1)$ and whose center lies on the line $x-3 y-11=0$.

Question 19

Find the equation of the circle which passes through the points $(2,-2)$ and $(3,4)$ and whose center is on the line $x+y=2$.

Question 20

Find the equation of the circle passing through the points $(4,1)$ and $(6,5)$ and having center on the line $4 x+y=16$.

Question 21

Find the equation of the circle which touches the axis of $y$ at a distance 4 from the origin and cuts off an intercept of length 6 on the axis of $x$.

Question 22

Does the point $(-2.5,3.5)$ lie inside outside or on the circle $x^{2}+y^{2}=25 ?$

Question 23

Find the centre and radius of each of the following circles :

(i) $x^{2}+y^{2}-8 x+10 y-12=0$

(ii) $x^{2}+y^{2}+8 x+10 y-8=0$

(iii) $2 x^{2}+2 y^{2}-x=0$

(iv) $x^{2}+y^{2}-4 x-8 y-45=0$

Question 24

Find the center and radius of each of the following circles :

(i) $x^{2}+(y-1)^{2}=2$

(ii) $\left(x-\frac{1}{2}\right)^{2}+\left(y+\frac{1}{3}\right)^{2}=\frac{1}{4}$

(iii) $x^{2}+y^{2}-2 x+4 y=8$

(iv) $x^{2}+y^{2}-4 x+6 y=5$