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[几何] 双曲线题目

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lrh2006 posted 2017-11-21 22:34 |Read mode
Last edited by hbghlyj 2025-5-4 10:17若过双曲线 $\frac{x^2}{a^2}-\frac{y^2}{9}=1(a>0)$ 的左焦点分别作双曲线的两条浙近线的平行线,则这两条平行线与双曲线的两条渐近线构成的四边形的面积的最小值为

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isee posted 2017-11-21 22:57
Last edited by isee 2017-11-21 23:11回复 1# lrh2006


    怕是没人来算答案,一眼看过去,就是纯算。

    这个似乎只是双曲线引出直线而已,猜一下,正方形时最值,即等轴双曲线时,此时的结果为9.

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kuing posted 2017-11-21 23:20
$c^2=a^2+9$, $2S=c\cdot kc=3c^2/a=3(a+9/a)\ge18$, $S\ge9$
还真是9……

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isee posted 2017-11-21 23:40


回复 3# kuing

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original poster lrh2006 posted 2017-11-22 14:32
回复 3# kuing


    嘻嘻,我跟你想的一模一样

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original poster lrh2006 posted 2017-11-22 14:33
谢谢两位咯

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original poster lrh2006 posted 2017-11-22 14:34
回复 2# isee


    嗯嗯,其实和双曲线没啥关系,我标题不当

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isee posted 2017-11-22 16:34
回复 7# lrh2006

标题没啥不当的,题目是双曲线啊。

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