If the circles `x^(2)+y^(2)+2gx+2fy=0` and `x^(2)+y^(2)+2g'x+2f'y=0` touch each other, then

Given that the circle x^(2)+y^(2)+2 x-4 y+4=0 and x^(2)+y^(2)-2 x-4 y-4=0 touch each other the equation of the common tangtnt is

If the circles x^(2)+y^(2)=9andx^(2)+y^(2)+2alphax+2y+1=0 touch each other internally , then alpha =

The circleS x^(2)+y^(2)+2 a x+c^2=0 and x^(2)+y^(2)+2 b y+c^2=0 touch if

The circles x^(2)+y^(2)+6 x+k=0 and x^(2)+y^(2)+8 y-20=0 touch each other internally. The value of k is

If the radical axis of the circles x^(2)+y^(2)+2gx + 2fy + c = 0 and 2x^(2) + 2y^(2) + 3x + 8y + 2c =0 touches the circle x^(2)+ y^(2)+2x+2y + 1 = 0, then

If the circles x^(2)+y^(2)-2 x-2 y-7=0 and x^(2)+y^(2)+4 x+2 y+k=0 cut orthogonally, then the length of the common chord of the circles is

Prove that the circle x^(2) + y^(2) + 2ax + c^(2) = 0 and x^(2) + y^(2) + 2by + c^(2) = 0 touch each other if (1)/(a^(2)) + (1)/(b^(2)) = (1)/(c^(2)) .

Given that the circleS x^(2)+y^(2)-2 x+6 y+6=0 and x^(2)+y^(2)-5 x+6 y+15=0 touch, the equation of their common tangtnt is

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)