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Gaokao Math Practice Question

5. (5 分) 已知 $M\left(x_{0}, y_{0}\right)$ 是双曲线 $C: \frac{x^{2}}{2}-y^{2}=1$ 上的一点, $F_{1}, F_{2}$ 是 $C$ 的左 、右两个焦点, 若 $\overrightarrow{M F_{1}} \cdot \overrightarrow{\mathrm{MF}_{2}}<0$, 则 $\mathrm{y}_{0}$ 的取值范围是( )

  1. A.$\left(\frac{\sqrt{3}}{3}, \frac{\sqrt{3}}{3}\right)$
  2. B.$\left(-\frac{\sqrt{3}}{6}, \frac{\sqrt{3}}{6}\right)$
  3. C.$\left(-\frac{2 \sqrt{2}}{3}, \frac{2 \sqrt{2}}{3}\right)$
  4. D.$\left(-\frac{2 \sqrt{3}}{3}, \frac{2 \sqrt{3}}{3}\right)$

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