The centres of a set of circles, each of radius 3, lie on the circle $x^2+y^2=25$. The locus of any point in the set is 

Let  $(h,k)$ be any point in the set, then equation of circle is ${(x-h)}^2+{(y-k)}^2=9$

then $h^2+k^2=25$

$\therefore 2\le$Distance between the centres of two circles $\le 8$

$\Rightarrow 2\le \sqrt{(h^2+k^2)}\le 8$

$4\le h^2+k^2\le 64$    $4\le h^2+k^2\le 64$

$\therefore locusof(h,k)is4\le x^2+y^2\le 64$  $\therefore locusof(h,k)is4\le x^2+y^2\le 64$   But $(h,k)lieon{x}^2+y^2=25$