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Gaokao Math Practice Question

已知直线 $y=k(x+2)(k>0)$ 与抛物线 $C: y^{2}=8 x$ 相交于 $A$ 、 $B$ 两点, $F$ 为 $C$ 的焦点, 若 $|F A|=2|F B|$, 则 $k=$（$\qquad$）

  1. A.$\frac{1}{3}$
  2. B.$\frac{\sqrt{2}}{3}$
  3. C.$\frac{2}{3}$
  4. D.$\frac{2 \sqrt{2}}{3}$

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