3. A line with an inclination angle of $60^{\circ}$ is drawn through the focus $F$ of the parabola $y^{2}=8(x+2)$. If this line intersects the parabola at points $A$ and $B$, and the perpendicular bisector of chord $A B$ intersects the $x$-axis at point $P$, then the length of segment $P F$ is
A. $\frac{16}{3}$
B. $\frac{8}{3}$
C. $\frac{16}{3} \sqrt{3}$
D. $8 \sqrt{3}$
3. $\mathrm{A}$ Hint: $F(0,0), A B$ equation is $y=\sqrt{3} x, A, B$ two points' x-coordinates satisfy: $3 x^{2}-8 x-16=0, A B$ midpoint $\left(\frac{4}{3}, \frac{4}{\sqrt{3}}\right)$, perpendicular bisector equation: $y-\frac{4}{\sqrt{3}}=-\frac{1}{\sqrt{3}}\left(x-\frac{4}{3}\right)$, let $y=0, P$ point's x-coordinate $x=4+\frac{4}{3}=\frac{16}{3},|P F|=\frac{16}{3}$.