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[几何] 2020年新高考全国卷1第22题 椭圆上的直角则斜边过定点

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isee posted 2020-7-13 16:10 |Read mode
2020年新高考全国卷1第22题

已知椭圆C:$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$的离心率为$\frac{\sqrt 2}2$,且过点$A(2,1)$.
(1)求$C$的方程:
(2)点$M$,$N$在$C$上,且$AM⊥AN$,$AD⊥MN$,$D$为垂足.证明:存在定点$Q$,使得$|DQ|$为定值.

(1)$x^2/6+y^2/3=1$;
(2)这是一道陈题改编,具体见楼下链接。

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original poster isee posted 2020-7-13 16:12

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