Find the equation and length of common tangent to hyperbola $\large\frac{x^2}{p^2}-\frac{y^2}{q^2}$$=1$ and $\large\frac{y^2}{p^2}-\frac{x^2}{q^2}$$=1$

Question

$\begin{array}{1 1}(a)\;x\mp y=\pm\sqrt{p^2-q^2},\sqrt 2\large\frac{p^2+q^2}{p^2-q^2}\\(b)\;x\mp y=\pm\sqrt{p^2+q^2},\sqrt 2\large\frac{p^2-q^2}{p^2+q^2}\\(c)\;x\pm y=\mp\sqrt{p^2-q^2},\sqrt 2\large\frac{p+q}{p^2-q^2}\\(d)\;\text{None of these}\end{array}$