Find the equation of the circle which passes through the points of intersection of circles `x^2 + y^2 - 2x - 6y + 6 = 0 and x^2 + y^2 + 2x – 6y + 6 = 0` and intersects the circle `x^2 + y^2 + 4x + 6y +4=0` orthogonally.

Find the equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0, x^2 + y^2 + 2x - 4y -6 = 0 and with its centre on the line y = x.

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

The equation of the circle passing through (1,2) and the points of intersection of the circles x^2+y^2-8x-6y+21=0 and x^2+y^2-2x-15=0 is

Find the equation of the circle which passes through the points (2,0)(0,2) and orthogonal to the circle 2x^2+2y^2+5x-6y+4=0 .

The equation of the circle which passes through the points of intersection of the circles x^(2)+y^(2)-6x=0 and x^(2)+y^(2)-6y=0 and has its centre at (3/2, 3/2), is

Tangents drawn from P(1, 8) to the circle x^2 +y^2 - 6x-4y - 11=0 touches the circle at the points A and B, respectively. The radius of the circle which passes through the points of intersection of circles x^2+y^2 -2x -6y + 6 = 0 and x^2 +y^2 -2x-6y+6=0 the circumcircle of the and interse DeltaPAB orthogonally is equal to

Find the equation of the circle passing through the points of intersections of circles x^2+y^2+6x+4y-12=0, x^2+y^2-4x-6y-12=0 , and having radius sqrt13 .

The equation of the circle which pass through the origin and cuts orthogonally each of the circles x^2+y^2-6x+8=0 and x^2+y^2-2x-2y=7 is

The equation of the circle passing through the point of intersection of the circles x^2 + y^2 - 6x + 2y + 4 = 0 and x^2 + y^2 + 2x - 6y - 6=0 and having its centre on y=0 is : (A) 2x^2 + 2y^2 + 8x + 3 = 0 (B) 2x^2 + 2y^2 - 8x - 3 = 0 (C) 2x^2 + 2y^2 - 8x + 3 = 0 (D) none of these

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.