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