Let $a$, $b$ be real numbers. The parabola $C: y = x^2 + ax + b$ in the coordinate plane has exactly 2 intersection points with the parabola $y = -x^2$, where the $x$-coordinate of one intersection point satisfies $-1 < x < 0$, and the $x$-coordinate of the other intersection point satisfies $0 < x < 1$.
[(1)] Illustrate in the coordinate plane the region of all possible points $(a,\, b)$.
[(2)] Illustrate in the coordinate plane the region through which the parabola $C$ can pass.
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Let $a$, $b$ be real numbers. The parabola $C: y = x^2 + ax + b$ in the coordinate plane has exactly 2 intersection points with the parabola $y = -x^2$, where the $x$-coordinate of one intersection point satisfies $-1 < x < 0$, and the $x$-coordinate of the other intersection point satisfies $0 < x < 1$.
\begin{enumerate}
\item[(1)] Illustrate in the coordinate plane the region of all possible points $(a,\, b)$.
\item[(2)] Illustrate in the coordinate plane the region through which the parabola $C$ can pass.
\end{enumerate}
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