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.

Show that the circles x^2 + y^2 + 2x-8y+8=0 and x^2 + y^2 + 10x - 2y+ 22=0 touch each other. Also obtain the equations of the two circles, each of radius 1, cutting both these circles orthogonally.

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

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.

If the circles x ^(2) + y ^(2) + 5x -6y-1=0 and x ^(2) + y^(2) +ax -y +1=0 intersect orthogonally (the tangents at the point of intersection of the circles are at right angles), the value of a is

Show that the circles x^(2)+y^(2)-6x+4y+4=0and x^(2)+y^(2)+x+4y+1=0 cut 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.

The locus of the centers of the circles which cut the circles x^(2) + y^(2) + 4x – 6y + 9 = 0 and x^(2) + y^(2) – 5x + 4y – 2 = 0 orthogonally is

Find the centre of the circle that passes through the point (1,0) and cutting the circles x^(2) + y ^(2) -2x + 4y + 1=0 and x ^(2) + y ^(2) + 6x -2y + 1=0 orthogonally is