When the circles `x^2 + y^2 + 4x + by + 3 = 0 and 2(x^2 + y^2) + 6x + 4y + C = 0` intersect orthogonally, then find the value of c is

If the two circle x^(2) + y^(2) - 10 x - 14y + k = 0 and x^(2) + y^(2) - 4x - 6y + 4 = 0 are orthogonal , find k.

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

The value of k for which the circles x^2 - y^2 + 3x - 7y +k = 0 and x^2 + y^2 - 4x + 2y - 14 = 0 would intersect orthogonallys

If the circle x^(2) + y^(2) + 8x - 4y + c = 0 touches the circle x^(2) + y^(2) + 2x + 4y - 11 = 0 externally and cuts the circle x^(2) + y^(2) - 6x + 8y + k = 0 orthogonally then k =

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

The locus of the centre of the circle which cuts the circles x^(2) + y^(2) + 4x - 6y + 9 = 0 " and " x^(2) + y^(2) - 4x + 6y + 4 = 0 orthogonally is