The locus of the centres of the circles which touch both the axes is given by

x^{2} - y^{2} = 0

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x^{2} + y^{2} = 0

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x^{2} - y^{2} = 1

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x^{2} + y^{2} = 1

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Solution

The correct option is A $x^{2} - y^{2} = 0$
Since, the circle touches both the axes, then $g = f$ .
$\Rightarrow g^{2} - f^{2} = 0$
$\Rightarrow x^{2} - y^{2} = 0$
Which is the required locus of the centres of the circles which touch both the axes.

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x^{2} + y^{2} = 16

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x^{2} + y^{2} = 16

x^{2} + y^{2} = 16 x

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