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1 Find centre and radius of circles given by 2 2 21 2 2 0m x y cx mcy

Sol:Given equation of the circle

( )

Centre (-g, -f) = (

)

And r= ( ) (

)

=

=()() =c

2 Find centre and radius of x2+y2+6x+8y-96=0.Sol: Given equation of the circle is x

2+y

2+6x+8y-96=0.

Compare with x2+y

2+2gx+2fy+c=0.

Centre (-g, -f) = (-3, -4)

Radius r=

=

()

()

=

3 Find the length of the tangent from (3, 3) to thecircle x

2+y

2+6x+8y+26=0.

Sol: Given equation of the circle is

x2+y

2+6x+8y+26=0.

Length of the tangent from (3, 3)= () () = =

4 Find the power of the point (3, 4) w. r. t the circlex

2+y

2-4x-6y-12=0.

Sol: Given equation of the circle is

x2+y

2+-4x-6y-12=0.

Power of the point is ()()=9+16-12-24-12=-23.

5

Find centre and radius of 3x

2

+3y

2

-6x+4y-4=0.Sol: Given equation of the circle is

3x2+3y

2-6x+4y-4=0.

( ) = .

6 If length of tangent from (2,5) to the circle

is

, then find k.

Sol: Length of the tangent from (2, 5)= () ()

S.O.B

k=-2

7 Obtain parametric equation of the circle Ifx

2+y

2-6x+4y-12=0, x

2+y

2+6x+8y-96=0.

Sol: centre (3, -2), c=-12

And r= () = Parametric equation of the circle

X= ,

8 If x2+y2-4x+6y+c=0 represents a circle with radius6, find the value of c.

Sol: centre (2, -3) and

r= () = S.O.B13+c=36=23.

9 If x2+y2-4x+6y+a=0 represents a circle with radius4, find the value of a.

Sol:

10 If x2+y2+6-8y+c=0 represents a circle with radius 6,find the value of c.

Sol:

11 If x2+y2+ax+by-12=0 is a circle with centre (2, 3),find the value of a, b and radius.

Sol: x2+y2+2ax+2by-12=0

Since centre (-, -

) = (2, 3)

a=-4 and b=-6Radius

r= () = =

12 If 3x2+2hxy+by2-5x+2y-3=0 represents a circle,find a, b.

Sol: If ax2+2hxy+by

2+2gx+2fy+c=0 represents a

circle then a=b and h=0

b=3 and h=0

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13 Find the equation of the circle with (1, 2), (4, 5) asends of a diameter.

Sol: the equation of the circle with ( ), ( ),as ends of a diameter.

Is (x-) (x-) +(y-) (y-) =0(x-1)(x-4)+(y-2)(y-5)=0

14 Find the equation of circle passing through (5, 6)and having centre (-1, 2).

Sol:

15 Find the equation of circle passing through (0, 0)and having centre (-1, 2).

Sol:

16 Find the equation of the circle passing through (2,3) and concentric with

01512822

yxyx .

Sol:17 Find the pole of x + y + 2 = 0 with respect to the

circle x2

+ y2 4x + 6y 12 = 0.

Sol:

18 Show that the points (4, -2), (3, -6) are conjugatew.r.to the circle x

2+y

2=24.

Sol:

19 If (4, k), (2, 3) are conjugate points with respectto the circle x

2+ y

2= 17 then find k.

Sol:

20 Show that the lines 01132 yx and0122 yx are conjugate with respect to the

circle 0126422

yxyx .

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