The center of the set of circles, each of radius 2, lie on the circle $x^{2} + y^{2} = 49$ . The locus of any point in the set is

9 \leq x^{2} + y^{2} \leq 81

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x^{2} + y^{2} \leq 25

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x^{2} + y^{2} \geq 25

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25 \leq x^{2} + y^{2} \leq 81

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Solution

The correct option is C $25 \leq x^{2} + y^{2} \leq 81$
Minimum distance from origin to any point on circle is $7 - 2 = 5$ .
Maximum distance from origin to any point on circle is $7 + 2 = 9$ .
$\Rightarrow 5 \leq \sqrt{x^{2} + y^{2}} \leq 9$
$\Rightarrow 25 \leq x^{2} + y^{2} \leq 81$

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