The equation of a circle of radius 1 touching the circles `x^2+y^2-2|x|=0` is (a) `x^2+y^2+2sqrt(2)x+1=0` (b) `x^2+y^2-2sqrt(3)y+2=0` (c) `x^2+y^2+2sqrt(3)y+2=0` (d) `x^2+y^2-2sqrt(2)+1=0`

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

The centre of the smallest circle touching the circles x^2+ y^2-2y -3=0 and x^2 +y^ 2-8x -18y +93= 0 is:

Suppose a x+b y+c=0 , where a ,ba n dc are in A P be normal to a family of circles. The equation of the circle of the family intersecting the circle x^2+y^2-4x-4y-1=0 orthogonally is (a) x^2+y^2-2x+4y-3=0 (b) x^2+y^2-2x+4y+3=0 (c) x^2+y^2+2x+4y+3=0 (d) x^2+y^2+2x-4y+3=0

Find the equation of radical axis of the circles x^(2)+y^(2)-3x+5y-7=0 and 2x^(2)+2y^(2)-4x+8y-13=0 .

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

If the represented by the equation 3y^2-x^2+2sqrt(3)x-3=0 are rotated about the point (sqrt(3),0) through an angle of 15^0 , on in clockwise direction and the other in anticlockwise direction, so that they become perpendicular, then the equation of the pair of lines in the new position is (a) y^2-x^2+2sqrt(3)x+3=0 (b) y^2-x^2+2sqrt(3)x-3=0 (c) y^2-x^2-2sqrt(3)x+3=0 (d) y^2-x^2+3=0

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)

Find the equation of the normal to the circle x^(2)+y^(2)=9 at the point (1//sqrt(2), 1// sqrt(2)) .

Find the equation of the circle which cuts the three circles x^2+y^2-3x-6y+14=0,x^2+y^2-x-4y+8=0, and x^2+y^2+2x-6y+9=0 orthogonally.