．已知平面区域\(\begin{cases}\begin{matrix}x\geqslant 0 \\ y\geqslant 0\end{matrix} \\ x+2y-4\leqslant 0\end{cases} \)恰好被面积最小的圆\(C\)\(:(\)\(x-a\)\()^{2}\)\(+\)\((\)\(y-b\)\()^{2}\)\(=r\)\({\,\!}^{2}\)及其内部所覆盖，则圆\(C\)的方程为          ．