Question

设双曲线(0＜a＜b)的半焦距为c,直线l过(a,0)、(0,b)两点,已知原点到直线l的距离为c,则双曲线的离心率为(　　)

A.2                       B.                          C.                          D.

Answer 1

解析:因为l:,所以原点到l的距离                 ①

又c²=a²+b²(0＜a＜b),                                                                                      ②

联立①②得ab=c².                                                                                     ③

③式两边除以a²,得

故,解得e=2或e=.

当e=时,a²=3b²,与a＜b矛盾.

所以e=2.

答案:A