Question

设F1和F2为双曲线x2/a2-y2/b2=1(a＞0,b＞0)的两个焦点，若F1,F2,

P(0,2b)是正三角形的三个顶点，则双曲线的离心率

Answer 1

tan60=2b/c ( tan60)2=(2b/c)2 3=4b2/c2 ,b2/c2=3/4 (c2-a2)/c2=3/4 1-a2/c2=3/4
a2/c2=1/4 c2/a2=4 c/a=2 e=2