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Gaokao Math Practice Question

椭圆 $C: \frac{x^{2}}{4}+\frac{y^{2}}{3}=1$ 的左、右顶点分别为 $A_{1}$、 $A_{2}$, 点 $P$ 在 $C$ 上且直线 $\mathrm{PA}_{2}$ 斜率的取值范围是 $[-2,-1]$, 那么直线 $\mathrm{PA}_{1}$ 斜率的取值范围是 ($\qquad$)

  1. A.$\left[\frac{1}{2}, \frac{3}{4}\right]$
  2. B.$\left[\frac{3}{8}, \frac{3}{4}\right]$
  3. C.$\left[\frac{1}{2}, 1\right]$
  4. D.$\left[\frac{3}{4}, 1\right]$

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