7. Given $B(-6,0), C(6,0)$ are two vertices of $\triangle A B C$, and the internal angles $A, B, C$ satisfy $\sin B-\sin C=$ $\frac{1}{2} \sin A$, then the equation of the locus of vertex $A$ is $\qquad$ .
7. $\frac{x^{2}}{9}-\frac{y^{2}}{27}=1$, and $x<-3$. Hint: By the Law of Sines, $|A C|-|A B|=\frac{1}{2}|B C|$, by the definition of a hyperbola.