9. Given the line $l: x=m y+q, m \neq 0$ intersects the ellipse $\Gamma: 3 x^{2}+4 y^{2}=12$ at two distinct points $\mathrm{A}$ and $\mathrm{B}$. Let $\mathrm{A}$'s reflection about the major axis of the ellipse be $A_{1}$, and $F$ be the right focus of the ellipse. Find the necessary and sufficient condition for $A_{1} 、 F 、 B$ to be collinear.
9. Analysis: Let $A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right)$, then $A_{1}\left(x_{1},-y_{1}\right)$, then $A_{1} 、 F 、 B$ being collinear is equivalent to $\operatorname{mom}_{A_{1} F}^{\operatorname{mom}}=\lambda A_{1} B$, i.e., $\frac{y_{1}}{y_{1}+y_{2}}=\frac{1-x_{1}}{x_{2}-x_{1}}$, simplifying to: $2 m y_{1} y_{2}=(1-q)\left(y_{1}+y_{2}\right)(*)$, combining the equations of line $l$ and ellipse $\Gamma$ yields: $\left(3 m^{2}+4\right) y^{2}+6 m q y+3 q^{2}-12=0$, by Vieta's formulas we have: $y_{1}+y_{2}=-\frac{6 m q}{3 m^{2}+4}, y_{1} y_{2}=\frac{3 q^{2}-12}{3 m^{2}+4}$, substituting into $(*)$ gives: $q=4$. Therefore, the necessary and sufficient condition is $q=4\left(m^{2}>4\right)$.