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

Distance of any point (x,y) on a circle with centre C lying on the circle ${\mathrm{x}}^2+{\mathrm{y}}^2=25$ and radius 3 from the origin

lies between OA and OB i.e between 2 and 8

$$\begin{gathered} \Rightarrow 2<\sqrt{x^2+y^2}<8 \\ \Rightarrow 4<x^2+y^2<64 \end{gathered}$$

$\therefore$ locus is $4\le {\mathrm{x}}^2+{\mathrm{y}}^2\le 64$