已知P是双曲线x^2/4-y^2/b^2 上一点,F1、F2是左右焦点,⊿P F1F2的三边长成等差数列,且∠F1 P F2=120 求e值
e是离心率-
人气：139 ℃ 时间：2019-10-24 11:04:29
解答
∠F1 P F2=120 °,F1F2最长,PF1-PF2=2a=4 2c+PF2=2PF1
===>PF1=2c-4,PF2=2c-8 PF1^2+PF2^2-2PF1PF2cos120°=F1F2^2
PF1= 2c-4,PF2=2c-8,代入得：8c^2-72c+112=0 c^2-9c+14=0 c=2（舍）或7
e=7/2
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