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.

For what value of k is the circle x^2 + y^2 + 5x + 3y + 7 = 0 and x^2 + y^2 - 8x + 6y + k = 0 cut each other orthogonally.

Show that the circles x^(2) +y^(2) - 2x - 4y - 20 = 0 and x^(2) + y^(2) + 6x +2y- 90=0 touch each other . Find the coordinates of the point of contact and the equation of the common tangent .

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

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)-6x+4y+4=0and x^(2)+y^(2)+x+4y+1=0 cut orthogonally.

Show that the circles x^(2) + y^(2) + 2 x -6 y + 9 = 0 and x^(2) +y^(2) + 8x - 6y + 9 = 0 touch internally.

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.

The locus of the centre of the circle cutting the circles x^2+y^2–2x-6y+1=0, x^2 + y^2 - 4x - 10y + 5 = 0 orthogonally is

The angle between the circles x^2+y^2-2x-4y+3=0 and x^2+y^2-4x-6y+11=0 is

Prove that the circle x^(2)+y^(2)+2x+2y+1=0 and circle x^(2)+y^(2)-4x-6y-3=0 touch each other.