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 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 =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'.

The length of the common chord of the circles x^(2) + y^(2) + 2gx + c = 0 and x^(2) + y^(2) + 2fy - c = 0 is

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

Circles x^(2)+y^(2)+2gx+2fy=0 and x^(2)+y^(2)+2g'x+2f'y=0 touch externally, if quad

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 =