The given system of equations is:
\[
\left\{
\begin{array}{r}
x^2 + y^2 = 8 \\
x^2 + y^2 + 4y = 0
\end{array}
\right.
\]
The first equation, \(x^2 + y^2 = 8\), represents a circle centered at the origin (0,0) with a radius of \(\sqrt{8} = 2\sqrt{2}\).
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