F1,F2分別為雙曲線的左右焦點,過點F2做此雙曲線的壹條漸近線的垂線,垂足為M,

設過F2(c,0)向漸進線y=b/ax作垂線,則有:MF2=|bc/a|/根號(b^2/a^2+1)=(bc/a)/(c/a)=b那麽有MF1=3b.MF2的斜率K=-a/b,則MF2的方程是y=-a/b(x-c)與y=b/ax聯立解得M坐標是:X=a^2/c,y=b/a*a^2/c=ab/c所以,MF1^2=(a^2/c+c)^2+(ab/c)^2=9b^2a^4/c^2+2a^2+c^2+a^2b^2/c^2=9b^2a^4+2a^2c^2+c^4+a^2b^2-9b^2c^2=0c^2=a^2+b^2代入得:a^4+2a^4+2a^2b^2+a^4+2a^2b^2+b^4+a^2b^2-9a^2b^2-9b^4=04a^4-4a^2b^2-8b^4=0a^4-a^2b^2-2b^2=0(a^2-2b^2)(a^2+b^2)=0即有:a^2-2b^2=0所以有:a^2=2b^2b^2/a^2=1/2b/a=根號2/2

所以,漸進線的方程是y=(+/-)根號2/2 X