Let the common tangent to the parabola
$y^{2}=4 x $ be
$y=m x+\frac{1}{m}$
It should be also touch the circle
$(x-3)^{2}+y^{2}= 9$
whose centre is (3,0) and radius $=3,$ then
$\frac{|3 m+1 / m|}{\sqrt{1+m^{2}}}=3$
$\Rightarrow 3 m^{2}=1$
$\Rightarrow m=\pm \frac{1}{\sqrt{3}}$
But $m>0$, then equation of common tangent is
$y =\frac{1}{\sqrt{3}} \cdot x+\sqrt{3}$
or $\sqrt{3} \cdot y =x +3$