The centres of a set of circles,each of radiu | vedclass

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(B) Let $C$ be the centre of a circle with radius $r = 2$. The centre $C$ lies on the circle $x^2 + y^2 = 36$,so the distance $OC = 6$,where $O$ is th

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$16 \leqslant x^2 + y^2 \leqslant 64$

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(B) Let $C$ be the centre of a circle with radius $r = 2$. The centre $C$ lies on the circle $x^2 + y^2 = 36$,so the distance $OC = 6$,where $O$ is the origin $(0, 0)$.For any point $P$ on the circle with centre $C$,the distance $OP$ satisfies $OC - r \le OP \le OC + r$.Substituting the values,we get $6 - 2 \le OP \le 6 + 2$,which simplifies to $4 \le OP \le 8$.Since $OP = \sqrt{x^2 + y^2}$,we have $4 \le \sqrt{x^2 + y^2} \le 8$.Squaring the inequality,we get $16 \le x^2 + y^2 \le 64$.

The centres of a set of circles,each of radius $2$,lie on the circle $x^2 + y^2 = 36$. The locus of any point in the set is -

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