雙曲線X^2/A2-Y^2/2=1(A＞根號(hào)2）
其漸近線為X^2/A2-Y^2/2=0,即Y=±√2/A X
A＞√2
Y=-√2/A X的斜率K1=-√2/A,-1＜K1＜0,令其與x軸夾角α
Y=√2/A X的斜率K2=√2/A,0＜K2＜1,令其與x軸夾角β
相當(dāng)每條漸近線與X軸的夾角都小于π/4
兩條漸近線的夾角為π/3
則β-α=π/3
tan(β-α) = tan(π/3)
(tanβ-tanα)/(1+tanβtanα) = tan(π/3)
(K2-K1)/(1+K2K1) = √3
(√2/A+√2/A)/(1-√2/A√2/A) = √3
2√2A/(A^2-2)=√3
√3A^2-2√2A-2√3=0
(√3A+√2)(A-√6)=0
A=√6
離心率e = √(A^2+B&2)/A = √(6+2)/√6 = 2√3/3