8. (10 points) Real numbers $a, b, x$ and $y$ are such that

$$
\left\{\begin{array}{l}
a x+b y=r-t \\
a x^{2}+b y^{2}=r \\
a x^{3}+b y^{3}=r+t \\
a x^{4}+b y^{4}=r+t^{2}
\end{array}\right.
$$

Find $a x^{2}+b y^{2}$.