The equation of the common tangent to the curves $y^2=8x$  and  $xy=-1$ is

Any tangent to y²=8x is y=mx+2/m. it will also tangent xy= -1 if $x[mx+\frac{2}{m}]=-1$ has equal roots $=\frac{4}{m^2}=4m\Rightarrow m=1,$ Hence tangent is y=x+2