The circle x2 + y2 + 2gx + 2 fy + c = 0 does not intersect x - axis, if

Given that the circle x2 + y2 + 2gx + 2fy + c = 0 does not intersect x - axis. We need to find the relation between g and c.


We know that the value of y on the x - axis is 0.


x2 + (0)2 + 2gx + 2f(0) + c = 0


x2 + 2gx + c = 0


The quadratic equation will have no roots if the circle does not intersect the x - axis.


We know that for the quadratic equation ax2 + bx + c = 0 the condition to be satisfied for the equal roots is b2 - 4ac<0


(2g)2 - 4(1)(c)<0


4(g2 - c)<0


g2 - c<0


g2<c


The correct option is (a).

17