A straight line touches the rectangular hyperbola $9x^2-9y^2=8$ and the parabola $y^2=32x.$ The equation of the line is

Let $y=mx+\frac{8}{m}$is a tangent to $y^2=32x$

$If it is a \tan gent to \frac{x^2}{{\displaystyle \frac{8}{9}}}-\frac{y^2}{\frac{8}{9}}=1 then$

$$\begin{gathered} c^2=a^2{m}^2-b^2 \\ \Rightarrow \frac{64}{m^2}=\frac{8}{9}{m}^2-\frac{8}{9} \\ \Rightarrow m^4-m^2-72=0 \\ \Rightarrow m^2=9 or m^2=-8 \\ \Rightarrow m=\pm 3 \end{gathered}$$