If the circle $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ touches x-axis , then

g = f

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g^{2} = c

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f^{2} = c

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g^{2} + f^{2} = c

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Solution

The correct option is A $g^{2} = c$
Given $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ touches x-axis
$\Rightarrow$ Radius $= | f |$
$\Rightarrow \sqrt{g^{2} + f^{2} - c} = | f |$
$\Rightarrow g^{2} + f^{2} - c = f^{2}$
$\Rightarrow g^{2} - c = 0$
$\Rightarrow g^{2} = c$ .

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