Two circles touch the parabola   and also touch x-axis. The equation of one direct common tangent of the two circles is 

$y^2=4x\Rightarrow 2y{y}^{\text{'}}=4\Rightarrow y^{\text{'}}=\frac{4}{2\left(2\right)}\Rightarrow y^{\text{'}}=1\Rightarrow$ tangent  


Common normal of two circles x+y-3=0
Since one common tangent is x-axis (y=0)
The other common tangent is x-3=0