在△ABC中\( ,\)已知A(\( －\)4\( ,\)0)\( ,\) B(4\( ,\)0)\( ,\)且\( \text{sinA}-\text{sinB}=\frac{1}{2}\text{sinC},\)则点C的轨迹方程为 ( )
A. \( \frac{{x}^{2}}{4}＋\frac{{y}^{2}}{12}=1\)
B. \( \frac{{x}^{2}}{4}-\frac{{y}^{2}}{12}=1(x＜-2)\) C. \( \frac{{x}^{2}}{12}-\frac{{y}^{2}}{4}=1\) D. \( \frac{{x}^{2}}{12}-\frac{{y}^{2}}{14}=1(y\ne 1)\)
