The circle `x^2+y^2+2gx+2fy+c=0` does not intersect x-axis , if (a) `g^2ltc` (b)`g^2gt c` (c) `g^2<2c` (d) none of these

Explanation

We have given the circle `x^2+y^2+2gx+2fy+c=0`

Since the circle intersects the x- axis, the equation of circle become

`x^{2}+2gx+c=0`

Now on solving this equation we have` D=\sqrt{4g^{2}-4c}\geq 0`

`\Rightarrow 4g^{2}-4c\geq 0`

`\Rightarrow g^{2}-c\geq 0`

`\Rightarrow g^{2}\geq c`

Therefore if `g^{2}\geq c` then the circle will not intersect the x-axis.

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