数学试题讲解

设椭圆

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1 (a > b > 0)

的左、右焦点分别为

F_{1} 、 F_{2}, P

是椭圆上一点,

| P F_{1} | = λ | P F_{2} |

\frac{1}{2} ⩽ λ ⩽ 2, ∠ F_{1} P F_{2} = \frac{π}{2}

, 则椭圆离心率的取值范围为

(0, \frac{\sqrt{2}}{2}]

[\frac{\sqrt{2}}{2}, \frac{\sqrt{5}}{3}]

[\frac{2}{3}, \frac{\sqrt{5}}{3}]

[\frac{\sqrt{5}}{3}, 1)