11. Let $A$ and $B$ be two distinct points on the parabola $C: y^{2}=4 x$, and $F$ be the focus of the parabola $C$. If $\overrightarrow{F A}=-4 \overrightarrow{F B}$, then the slope of the line $A B$ is ().
(A) $\pm \frac{2}{3}$
(B) $\pm \frac{3}{2}$
(C) $\pm \frac{3}{4}$
(D) $\pm \frac{4}{3}$
11. D.

Let $A\left(x_{1}, y_{1}\right), B\left(x_{2}, y_{2}\right)$.
From $\overrightarrow{F A}=-4 \overrightarrow{F B} \Rightarrow y_{1}=-4 y_{2}$.
Let $l_{A B}: y=k(x-1)$, and combine with the parabola to get
$$
\begin{array}{l}
k y^{2}-4 y-4 k=0 \\
\Rightarrow y_{1}+y_{2}=\frac{4}{k}, y_{1} y_{2}=-4 .
\end{array}
$$

Combining equations (1) and (2) yields $k= \pm \frac{4}{3}$.