If a rectangular hyperbola `(x-1)(y-2)=4` cuts the circle `x^(2)+y^(2)+2gx+2fy+c=0` at points (3,4), (2,6), (-1,0) and (-3,1), then the value of `(g+f)` is equal to

If a rectangular hyperbola (x-1)(y-2)=4 cuts a circle x^(2)+y^(2)+2gx+2fy+c=0 at points (3, 4), (5, 3), (2, 6) and (-1, 0) , then the value of (g+f) is equal to

If the circle x ^(2) + y^(2) + 2gx + 2fy+ c=0 touches X-axis, then

The equation of the normal at P(x_(1),y_(1)) to the circle x^(2)+y^(2)+2gx+2fy+c=0 is

If the circle x^(2)+y^(2)+2gx+2fy+c=0 touches x- axis at (x_(1),0) then x^(2)+2gx+c =

If alpha is the angle subtended at P(x_(1),y_(1)) by the circle S-=x^(2)+y^(2)+2gx+2fy+c=0 then

If the circle x^(2)+y^(2)+2gx+2fy+c=0 touches y -axis then the condition is

If the origin lies inside the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 , then

Let O be the origin and P be a variable point on the circle x^(2)+y^(2)+2x+2y=0 .If the locus of mid-point of OP is x^(2)+y^(2)+2gx+2fy=0 then the value of (g+f) is equal to -