If the two circles `x^2+y^2+2gx + c =0` and `x^2+y^2-2fy -c =0` have equal radius then locus of (g,f) is

If two circleS x^(2)+y^(2)+2 lambda x+c=0 and x^(2)+y^(2)-2 mu y-c=0 have equal radius then the locus of (lambda, mu) is

if the two circles x^2 + y^2 + 2gx + 2fy = 0 and x^2 + y^2 + 2g'x + 2 f'y = 0 touch each other then show that f'g = fg'

If two cricles x^2 + y^2 + 2gx + 2fy = 0 and x^2 +y^2 + 2g'x + 2f'y = 0 touch each other, then

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

If the circles x^2 + y^2 + 2gx + 2fy + c = 0 bisects x^2+y^2+2g'x+2f'y + c' = 0 then the length of the common chord of these two circles is -

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

If two circle x^(2)+y^(2)+2gx +2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch each other then f'g =fg'.

If circles x^(2) + y^(2) + 2gx + 2fy + c = 0 and x^(2) + y^(2) + 2x + 2y + 1 = 0 are orthogonal , then 2g + 2f - c =