`fy=|x|`

The equation of the tangent to circle x^(2)+y^(2)+2g x+2fy=0 at origin is :

The equation of the tangent to circle x^(2)+y^(2)+2g x+2fy=0 at origin is :

I fy=sec^(- 1)((x+1)/(x-1))+sin^(- 1)((x-1)/(x+1)),t h e n(dy)/(dx)

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'

circle ax^(2)+ay^(2)+2gx+2fy+c=0 touches X -axis,if

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 .