．已知圆\(M\)\(:\)\(x\)\({\,\!}^{2}\)\(+y\)\({\,\!}^{2}\)\(+\)\(2\)\(mx-\)\(3\)\(=\)\(0(\)\(m < \)\(0)\)的半径为\(2\)，椭圆\(C\)\(: \dfrac{{x}^{2}}{{a}^{2}}+ \dfrac{{y}^{2}}{3} \)\(=\)\(1\)的左焦点为\(F\)\((\)\(-c\)，\(0)\)，若垂直于\(x\)轴且经过\(F\)点的直线\(l\)与圆\(M\)相切，则\(a\)的值为\((\) \()\)