Find the equations of the two circles which intersect the circles
`x^(2)+y^(2)-6y+1=0andx^(2)+y^(2)-4y+1=0`
orthogonally and touch the line 3x+4y+5=0`.

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 the circle which cuts the circles x^2+y^2-4x-6y+11=0 and x^2+y^2-10x-4y+21=0 orthogonally and has the diameter along the line 2x+3y=7.

Find the equation of the circle passing through the intersection of the circles x^2 + y^2-4 = 0 and x^2+y^2-2x-4y+4=0 and touching the line x + 2y=0

Find the equation of the circle which cuts the circles x^2+y^2+4x+2y+1=0, 2(x^2+y^2)+8x+6y-3=0 and x^2+y^2+6x-2y-3=0 orthogonally.

Find the equation of the circle which cuts the three circles x^2+y^2-3x-6y+14=0,x^2+y^2-x-4y+8=0, and x^2+y^2+2x-6y+9=0 orthogonally.

Find the equation of the family of circles touching the lines x^2-y^2+2y-1=0.

The equation of the circle which cuts the three circles x^2+y^2-4x-6y+4=0, x^2+y^2-2x-8y+4=0, x^2+y^2-6x-6y+4=0 orthogonally is

Find the angle of intersection of the circles x^2+y^2-6x+4y+11=0andx^2+y^2-4x+6y+9=0

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.

Equation of the circle which cuts the circle x^2+y^2+2x+ 4y -4=0 and the lines xy -2x -y+2=0 orthogonally, is