9. Let $F_{1}$ and $F_{2}$ be the left and right foci of the hyperbola $C: \frac{x^{2}}{9}-\frac{y^{2}}{27}=1$, and let point $A\left(\frac{9}{2}, \frac{\sqrt{135}}{2}\right)$. Then the coordinates of point $M$, where the angle bisector of $\angle F_{1} A F_{2}$ intersects the $x$-axis, are ( ).
(A) $(2,0)$
(B) $(-2,0)$
(C) $(4,0)$
(D) $(-4,0)$
9. A.

Notice,
$$
\begin{array}{l}
F_{1}(-6,0), F_{2}(6,0) \\
\Rightarrow \frac{\left|A F_{1}\right|}{\left|A F_{2}\right|}=2 \Rightarrow \frac{\left|M F_{1}\right|}{\left|M F_{2}\right|}=2 \Rightarrow M(2,0) .
\end{array}
$$