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.

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

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 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 equation of the circle passing through the points of intersection of the circles x^(2)+y^(2)+6x+4y-12=0 , x^(2)+y^(2)-4x-6y-12=0 and having radius sqrt(13) is

The equation of the circle passing through the points of intersection of the circles x^(2)+y^(2)+6x+4y-12=0 , x^(2)+y^(2)-4x-6y-12=0 and having radius sqrt(13) is

If the equation of the circle throught the points of intersection of the circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+"Ax"+"By"+C=0 and intersecting the circle x^(2)+y^(2)-2x-4=0 orthogonally is x^(2)+y^(2)+"Ax"+"By"+C=0 , then find teh value of (A+B+C) .

Find the equation of the circle which passes through the point (1, 1) & which touches the circle x^(2) + y^(2) + 4x – 6y – 3 = 0 at the point (2, 3) on it.