k=tan30=√3/3
设直线方程：y=√3(x-c)/3
则：x^2/a^2-(x-c)^2/3b^2=1
3(c^2-a^2)x^2-a^2(x-c)^2=3a^2(c^2-a^2)
(3c^2-4a^2)x^2+2a^2cx-4a^2c^2+3a^4=0
只有一个交点
3c^2-4a^2=0,c^2/a^2=4/3,e=c/a=2√3/3
或
判别式△=4a^4c^2-4(3c^2-4a^2)(3a^4-4a^2c^2)
=48a^2(c^4+a^4-2a^2c^2)
=48a^2(a^2-c^2)^2
=0
a^2=c^2
不成立
所以,双曲线离心率e=2√3/3