两条渐近线的夹角为π/3,双曲线x^2/a^2-y^2/2=1.求离心率...

问题描述:

两条渐近线的夹角为π/3,双曲线x^2/a^2-y^2/2=1.求离心率...

夹角为π/3
有两种
则一条渐近线倾斜角是π/3或π/6
b/a=tanπ/3=√3
b=√3a
c²=a²+b²=4a²
c=2a
e=c/a=2
b/a=tanπ/3=√3/3
b=√3a/3
c²=a²+b²=4a²/3
c=2√3a/3
e=c/a=2√3/3