The center of a circle, each of radius $3,$ be on the circle $x^{2} + y^{2} = 25.$ The locus of any point in the set is

4 \leq x^{2} + y^{2} \leq 64

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

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

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

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Solution

The correct option is B $x^{2} + y^{2} \leq 25$
$x^{2} + y^{2} = 5^{2}$
Centre(0,0)
radius=5 units
$r_{1} = 5 - 3 = 2 u n i t s$
$r_{2} = 5 + 3 = 8 u n i t s$
$∴$ locus is
${r_{1}}^{2} \leq (x - 0)^{2} + (y - 0)^{2} \leq {r_{2}}^{2} 4 \leq x^{2} + y^{2} \leq 64$

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