9. Given real numbers $a$, $b$, $x$, $y$ satisfy $a x+b y=3$, $a y-b x=5$. Then the value of $\left(a^{2}+b^{2}\right)\left(x^{2}+y^{2}\right)$ is $\qquad$.
9. 34 .
$$
\begin{array}{l}
\left(a^{2}+b^{2}\right)\left(x^{2}+y^{2}\right) \\
=a^{2} x^{2}+a^{2} y^{2}+b^{2} x^{2}+b^{2} y^{2} \\
=\left(a^{2} x^{2}+b^{2} y^{2}+2 a b x y\right)+\left(a^{2} y^{2}+b^{2} x^{2}-2 a b x y\right) \\
=(a x+b y)^{2}+(a y-b x)^{2} \\
=3^{2}+5^{2}=34 .
\end{array}
$$