Gaokao Math Practice Question
已知双曲线 $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a>0, b>0)$ 的右焦点与抛物线 $y^{2}=2 p x(p>0)$ 的焦点重 合, 抛物线的准线交双曲线于 $A, B$ 两点, 交双曲线的渐近线于 $C 、 D$ 两点, 若 $|C D|=\sqrt{2}|A B|$. 则双曲线的离心率为 ($\quad$)
- A.$\sqrt{2}$
- B.$\sqrt{3}$
- C.$2$
- D.$3$
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