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幼苗
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F2(1,0)设过F2的直线方程是x=my+1
代入到椭圆中有:4(m^2y^2+2my+1)+5y^2-20=0
(4m^2+5)y^2+8my-16=0
y1+y2=-8m/(4m^2+5),y1y2=-16/(4m^2+5)
|y1-y2|=根号[64m^2/(4m^2+5)^2+64/(4m^2+5)]=根号(64m^2+256m^2+320)/(4m^2+5)^2=8/(4m^2+5)*根号[5(m^2+1)]
S(AOB)=1/2OF2*|y1-y2|=4/(4m^2+5)*根号[5m^2+5]
下面计算出S的最大值就行了,明天再做,今天没有时间了.
1年前
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