The circles `x^2 + y^2 + 6x + 6y = 0` and `x^2 + y^2 - 12x - 12y = 0`

Let find the radical and centre of the circles x^2 + y^2 - 2x + 6y = 0 " ___"(1) x^2 + y^2 - 4x - 2y + 6 = 0 " ____"(2) and x^2 + y^2 -12x + 2y + 3 = 0 "___"(3)

The radical centre of the circles x^(2) + y^(2)- 2x + 6y = 0 , x^(2) + y^(2) - 4x - 2y + 6 = 0 , x^(2) + y^(2) - 12x + 12y + 30 = 0 is

If the angle between the circles x^2 + y^2 - 12x - 6y + 41 = 0 and x^2 + y^2 + kx + 6y - 59 = 0 is 45^@ find k.

The distance from (1,2) to the radical axis of the circles x^(2) + y^(2) + 6x -16 = 0 , x^(2) + y^(2) - 2x - 6y - 6 = 0 is

Prove that the radii of circles x^2 + y^2 = 1, x^2 + y^2 - 2x -6y = 6 and x^2 + y^2 - 4x - 12y = 9 are in A.p.

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

Find the equation of circle passing through the origin and cutting the circles x^(2) + y^(2) -4x + 6y + 10 =0 and x^(2) + y^(2) + 12y + 6 =0 orthogonally.

Find the equation of the radical axis of the following circles. x^2 + y^2 + 4x + 6y -7 = 0. 4(x^2 + y^2) + 8x + 12y - 9 = 0.