4. Given the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$ with the right focus at $F$, the right directrix at $l$, and a line intersecting the two branches of the hyperbola at points $P$ and $Q$, and intersecting $l$ at $R$. Then ( ).
( A) $\angle P F R>\angle Q F R$
( B) $\angle P F R<\angle Q F R$
( C) $\angle P F R=\angle Q F R$
(D) The size of $\angle P F R$ and $\angle Q F R$ is uncertain
4. ( C ).

As shown in Figure 2, draw $P P^{\prime} \perp l$ and $Q Q^{\prime} \perp l$, with the feet of the perpendiculars being $P^{\prime}$ and $Q^{\prime}$, respectively. By the properties of similar triangles, we get
$$
\frac{|P R|}{|R Q|}=\frac{\left|P P^{\prime}\right|}{\left|Q Q^{\prime}\right|} \text {. }
$$

Also, by the second definition of a hyperbola, we have
$$
\frac{|P F|}{\left|P P^{\prime}\right|}=e=\frac{|Q F|}{\left|Q Q^{\prime}\right|} .
$$

Thus, $\frac{|P R|}{|R Q|}=\frac{|P F|}{|Q F|}$.
Therefore, $F R$ bisects $\angle P F Q$.