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[几何] 这个解析几何极点极线那些理论能否用上?

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Tesla35 Posted 2019-6-26 21:42 |Read mode
(2018金华十校高二上期末)已知椭圆$C:\frac{x^2}{a^2}+\frac{y^2}{b^2}=1(a>b>0)$,右焦点$F_2(2,0)$,点$(\sqrt{3},1)$在椭圆上.
(1)求椭圆的方程;
(2)设$P(x_0,y_0)(y_0>0)$为椭圆$C$上一点,过焦点$F_1,F_2$的弦分别为$PA,PB$,设$\vv{PF_1}=\lambda_1\vv{F_1A},\vv{PF_2}=\lambda_2\vv{F_2B}$,若$\lambda_1=2$,求$\lambda_2$的值.

第一问答案:
$\frac{x^2}{6}+\frac{y^2}{2}=1.$

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kuing Posted 2019-6-26 21:54
利用 1/FP+1/FA=2/(ep) 来做就很简单啊,所有线长都能算出来……

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