hbstt
幼苗
共回答了20个问题采纳率:95% 举报
![](https://img.yulucn.com/upload/b/27/b27ff1b0274dc7252101f6bfe9dbb019_thumb.jpg)
,
(1)由双曲线的定义可知,曲线
![](https://img.yulucn.com/upload/6/06/606d08aead0910a8b16789d3357d94ff_thumb.jpg)
是以
![](https://img.yulucn.com/upload/e/c7/ec7a86a771de7798cb0861b2f4c971e4_thumb.jpg)
为焦点的双曲线的左支,且
![](https://img.yulucn.com/upload/f/93/f9313a10431742e078e7b261de9a914b_thumb.jpg)
,易知b=1,故曲线
![](https://img.yulucn.com/upload/6/06/606d08aead0910a8b16789d3357d94ff_thumb.jpg)
的方程为
![](https://img.yulucn.com/upload/a/a4/aa4d80c6a8b91ec764f1eed6f5175783_thumb.jpg)
.…2分
设
![](https://img.yulucn.com/upload/6/b1/6b1bf9870220cec837384350438a8bbe_thumb.jpg)
,由题意建立方程组
消去y,得
![](https://img.yulucn.com/upload/9/03/9031a3d6041c2b5d5836b993afd6597d_thumb.jpg)
.又已知直线与双曲线左支交于两点A,B,有
解得
![](https://img.yulucn.com/upload/b/27/b27ff1b0274dc7252101f6bfe9dbb019_thumb.jpg)
.…………6分
(2)∵
![](https://img.yulucn.com/upload/f/ae/fae4bf20244daf9bc1e83e1e89e7b8f4_thumb.jpg)
依题意得
![](https://img.yulucn.com/upload/1/42/142a02e344e3b59694dfce201a475931_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/d9/ad985228cd0b6ee3c9d1d74cf64622b8_thumb.jpg)
整理后得
![](https://img.yulucn.com/upload/7/57/75764c068e04140be0e72929418e7b56_thumb.jpg)
.
∴
但
![](https://img.yulucn.com/upload/b/27/b27ff1b0274dc7252101f6bfe9dbb019_thumb.jpg)
, ∴
![](https://img.yulucn.com/upload/1/ef/1ef3d5f36cb457d5cd064ecddadc9caf_thumb.jpg)
.
故直线
![](https://img.yulucn.com/upload/5/db/5db4b51ed7cbe810b082d894c46b7f59_thumb.jpg)
的方程为
![](https://img.yulucn.com/upload/4/83/4835a79a7ea4a18a17d47fbd26ac35b5_thumb.jpg)
……………8分
设
![](https://img.yulucn.com/upload/1/60/16071c7b86825a946df3f11cd421ae42_thumb.jpg)
,由已知
![](https://img.yulucn.com/upload/b/6b/b6bf3c3700d1e86f12c2873ef6a36028_thumb.jpg)
得
![](https://img.yulucn.com/upload/7/b2/7b21222965c4a4f66622664a275740bc_thumb.jpg)
,
∴
![](https://img.yulucn.com/upload/8/29/829a445e3ab2c91a549758255e0232d9_thumb.jpg)
=
![](https://img.yulucn.com/upload/c/5a/c5a56182ef8b4b717136879cb4064d93_thumb.jpg)
,
![](https://img.yulucn.com/upload/f/09/f0940f39099cebcdf80fab5ec66d8310_thumb.jpg)
.
![](https://img.yulucn.com/upload/7/67/767781dde47b068f23847ffd7e57ca55_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/2c/a2ccee151fe5230dbb2e635fb3d78776_thumb.jpg)
,
∴点
.
![](https://img.yulucn.com/upload/7/6d/76df44673959a7c46512b8fd66e6fa2c_thumb.jpg)
将点C的坐标代入曲线E的方程,得
但当m=-4时,所得的点在双曲线的右支上,不合题意
∴
![](https://img.yulucn.com/upload/e/3f/e3f79b18d00b0a5d0b14c9ff0d06afec_thumb.jpg)
,点C的坐标为
![](https://img.yulucn.com/upload/b/4a/b4a36934af798800baa41210ddbcb374_thumb.jpg)
。…………12分
1年前
5