mhxt1986
幼苗
共回答了18个问题采纳率:77.8% 举报
F(0.5p,0)
A(2pa^2,2pa),B(2pb^2,2pb)
M(pa^2+pb^2,pa+pb)
k(AF)=2a/(2a^2-0.5),k(BF)=2b/(2b^2-0.5)
[k(AF)-k(BF)]/[1+k(AF)*k(BF)]=- √3
a-b=√3*(4a^2^b^2-a^2-b^2+4ab+0.25).(1)
AB^2=4p^2*(a-b)^2*(a^2+b^2+2ab+1)
MN^2=p^2*(a^2+b^2+0.5)
d^2=MN^2/AB^2=p^2*(a^2+b^2+0.5)^2/[4p^2*(a-b)^2*(a^2+b^2+2ab+1)]
a=b,MN/AB有最大值
|MN|=|AF|
(|AB|/2)/|AF|=√3/2
(|MN|/|AB|)max=1/√3
1年前
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