解由e=2
即c/a=2
即c^2=4a^2
即a^2+b^2=4a^2
即b^2=3a^2
故双曲线x^2/a^2-y^2/b^2=1
变为双曲线x^2/a^2-y^2/3a^2=1
令x^2/a^2-y^2/3a^2=0
即y^2=3x^2
即y=±√3x
故渐近线方程y=±√3x