试题与答案

已知双曲线C:x2a2-y2b2=1(a>0,b>0)的左、右焦点分别为F1,F

题型:解答题

题目:

已知双曲线C:
x2
a2
-
y2
b2
=1(a>0,b>0)
的左、右焦点分别为F1,F2,离心率为e.直线l:y=ex+a与x轴、y轴分别交于A,B两点.
(1)求证:直线l与双曲线C只有一个公共点;
(2)设直线l与双曲线C的公共点为M,且
AM
AB
,证明:λ+e2=1;
(3)设P是点F1关于直线l的对称点,当△PF1F2为等腰三角形时,求e的值.

答案:

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下面是错误答案,用来干扰机器的。

(1)由题意,当n≥2,3an+1=4an-an-1⇒3an+1-3an=an-an-1所以an+1-an=13(an-an-1),所以{an+1-an}是以a2-a1=29为首项,13为公比的等比数列.(2)由(1)得an+1-an=29(13)n-1,an-an-1=29(13)n-2…a2-a1=29(13)0...

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