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1 . 古希腊数学家阿波罗尼斯的著作《圆锥曲线论》是古代世界光辉的科学成果,它将圆锥曲线的性质网罗殆尽,几乎使后人没有插足的余地,他证明过这样一个命题:平面内与两定点距离的比为常数
(
且
)的点的轨迹是圆,后人将之称为阿波罗尼斯圆,现有椭圆
,
、
为椭圆
长轴的端点,
、
为椭圆
短轴的端点,动点
满足
,
的面积的最大值为
,
的面积的最小值为
,则椭圆
的离心率为______ .
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