The equation of the common tangent touching the circle ${(x-3)}^2+y^2=9$ and the parabola $y^2=4x$  above the x-axis is:

A tangent to parabola  $y^2=4xisy=mx+\frac{1}{m}\Rightarrow m^{2}x-my+1=0$
If touches the circle  ${(x-3)}^2+y^2=9$
If  $\frac{3m^2+1}{\sqrt{m^4+m^2}}=3$
$\Rightarrow 9m^4+6m^2+1=9m^4+9m^2$ 
m is infinite or  $m=\pm \frac{1}{\sqrt{3}}$
Tangents are x=0 and  $y=\pm \frac{1}{\sqrt{3}}x\pm \sqrt{3}$
Tangents above the axis is  $y=\pm \frac{1}{\sqrt{3}}x\pm \sqrt{3}$
$\Rightarrow \sqrt{3}y=x+3$