If $g^{2} + f^{2} = c,$ then the equation $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ will represent

A circle of radius g

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A circle of radius f

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A circle of diameter $\sqrt{c}$

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A circle of radius 0

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Solution

The correct option is D A circle of radius 0
Radius of given circle = $\sqrt{g^{2} + f^{2} - c}$
$g^{2} + f^{2} - c$ (given), $∴$ Radius = 0.

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