Find the angle at which the circles ` x^(2) + y^(2) + x + y = 0 and x^(2) + y^(2) + x - y = 0 ` intersect

The value of k, if the circles 2x ^(2) + 2y ^(2) - 4x + 6y = 3 and x ^(2) + y ^(2) + kx + y =0 cut orthogonally is

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

The locus of a point which moves so that the ratio of the length of the tangents to the circles x^(2)+ y^(2)+ 4x+3 =0 and x^(2)+ y^(2) -6x +5=0 is 2 : 3 is a) 5x^(2) +5y^(2) - 60x +7=0 b) 5x^(2) +5y^(2) +60x -7=0 c) 5x^(2) +5y^(2) -60x -7=0 d) 5x^(2) +5y^(2) +60x +7=0

Find the value of p so that the three lines 3x + y - 2 = 0, px + 2y - 3 = 0 and 2x - y -3 = 0 may intersect at a point.

If the circles x^(2) +y^(2) + ax -6y + 4 =0 and x^(2) + y^(2) - 12x + 32 =0 touch externally each other and if the distance between the centres is equal to 5, then the values of a are