Question 81
Find all real numbers $a$ and $b$ such that the system
$$
\begin{cases}
x + a = y + b \\
x^2 - a = 2y
\end{cases}
$$
has a unique solution $(x_0, y_0)$ and it satisfies the equality $x_0^2 + y_0^2 = 1025$.
$$
\begin{cases}
x + a = y + b \\
x^2 - a = 2y
\end{cases}
$$
has a unique solution $(x_0, y_0)$ and it satisfies the equality $x_0^2 + y_0^2 = 1025$.