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 (-2,14) and concentric with the circle x^(2)+y^(2)-6x-4y-12=0

Find the equation of the circle passing through the points of intersection of the circles x^2 + y^2 - 2x - 4y - 4 = 0 and x^2 + y^2 - 10x - 12y +40 = 0 and whose radius is 4.

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 radius of the circle x^(2) + y^(2) + 4x - 6y + 12 = 0 is

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

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 circles x^(2)+y^(2)-4x-6y-12=0 and x^(2)+y^(2)+4x+6y+4=0

Show that the circles x^2 + y^2 - 2x-6y-12=0 and x^2 + y^2 + 6x+4y-6=0 cut each other orthogonally.

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

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