(本题满分14分)本题共有2个小题,第1小题满分6分,第2小题满分8分.
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/30 07:17:37
(本题满分14分)本题共有2个小题,第1小题满分6分,第2小题满分8分. 已知双曲线 ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() (1)用 ![]() ![]() (2)求△ ![]() ![]() |
(1)由已知,
,
(
,
),设
由
0 ,
得
,故
点的坐标为
,…(3分)
将
点的坐标代入
,化简得,
.…………(3分)
(2)解法一:设
,则
,所以
.……(1分)
又
,
,所以
,…………(3分)
记
,
,则
在
上是减函数,在
上是增函数.…………(2分)
所以,当
时,
取最小值
,当
时,
取最大值
.
所以△
面积的取值范围是
.…………(2分)
解法二:因为
,
(
,
),所以
,…(4分)
记
,![](http://img.wesiedu.com/upload/3/5a/35a61e59371d3a7594ee15fa9e5f8e6e.jpg)
![](http://img.wesiedu.com/upload/2/da/2da5397fb0f755ca46cdfee02f3abff6.jpg)
![](http://img.wesiedu.com/upload/a/0d/a0d05b54682b64e3b5276f44cbed8de9.jpg)
![](http://img.wesiedu.com/upload/d/99/d9992ebc702a294f83cf9275180f9d35.jpg)
![](http://img.wesiedu.com/upload/9/a9/9a94fe2a637a3c46f1f86d79fa1ceff4.jpg)
![](http://img.wesiedu.com/upload/4/f6/4f66a95622578545332850455537d95d.jpg)
由
![](http://img.wesiedu.com/upload/a/f4/af41c3bf397925d41d7f0a38d4bc6617.jpg)
![](http://img.wesiedu.com/upload/d/c5/dc552114453414311dadd9da650d110c.jpg)
![](http://img.wesiedu.com/upload/e/37/e37f7a87fc252d60ec5d8c2d5a8a5fff.jpg)
![](http://img.wesiedu.com/upload/2/89/289472b2c882e97e66321539da22a679.jpg)
![](http://img.wesiedu.com/upload/b/0d/b0d4384d0d6bf2d370373d3266a73e8f.jpg)
将
![](http://img.wesiedu.com/upload/2/89/289472b2c882e97e66321539da22a679.jpg)
![](http://img.wesiedu.com/upload/6/f3/6f3961e5fc93677f6c8ddc41b46656f1.jpg)
![](http://img.wesiedu.com/upload/c/02/c02dc0457c685f405627ce95d1b8345c.jpg)
(2)解法一:设
![](http://img.wesiedu.com/upload/2/16/2164cdad880557e5083d832f9baa366c.jpg)
![](http://img.wesiedu.com/upload/1/07/107daa5781778e3daf1bc5cd5b2b697d.jpg)
![](http://img.wesiedu.com/upload/5/6f/56f9753057af7f9c3ffc2634702e473f.jpg)
又
![](http://img.wesiedu.com/upload/7/ab/7abecb4a4298dd96eac8355c95387cf8.jpg)
![](http://img.wesiedu.com/upload/6/da/6dae0f6398120b2d0796669787dffe6b.jpg)
![](http://img.wesiedu.com/upload/7/7b/77b41503426b1676a929b69436a47bb9.jpg)
![](http://img.wesiedu.com/upload/4/ab/4abb8a5fda664c9c26e2c01b23742585.jpg)
记
![](http://img.wesiedu.com/upload/2/4a/24aa56b958eb062b241100c9b120555f.jpg)
![](http://img.wesiedu.com/upload/3/5a/35a61e59371d3a7594ee15fa9e5f8e6e.jpg)
![](http://img.wesiedu.com/upload/7/4a/74a8276fbd1d47116fb2eefa4af74608.jpg)
![](http://img.wesiedu.com/upload/9/0b/90bbc3c2d43d96d3780b14e4fb94dd66.jpg)
![](http://img.wesiedu.com/upload/b/ac/bacea4656ceb3536525318b5da02274a.jpg)
所以,当
![](http://img.wesiedu.com/upload/4/10/410f0380440158bfe85ab8df8e0eca16.jpg)
![](http://img.wesiedu.com/upload/7/4a/74a8276fbd1d47116fb2eefa4af74608.jpg)
![](http://img.wesiedu.com/upload/8/31/831a946f9cff0c6abc9f57a7cdb87a9e.jpg)
![](http://img.wesiedu.com/upload/9/81/9816c7a79afa12a9be5480032c705c80.jpg)
![](http://img.wesiedu.com/upload/7/4a/74a8276fbd1d47116fb2eefa4af74608.jpg)
![](http://img.wesiedu.com/upload/3/35/33523ae145108be7c6c78fc4a9b73600.jpg)
所以△
![](http://img.wesiedu.com/upload/0/09/009a38c5c8f66175dda4d15b84d33dea.jpg)
![](http://img.wesiedu.com/upload/e/38/e3879b3a098719b33f0a118d70611fb9.jpg)
解法二:因为
![](http://img.wesiedu.com/upload/2/da/2da5397fb0f755ca46cdfee02f3abff6.jpg)
![](http://img.wesiedu.com/upload/a/0d/a0d05b54682b64e3b5276f44cbed8de9.jpg)
![](http://img.wesiedu.com/upload/d/99/d9992ebc702a294f83cf9275180f9d35.jpg)
![](http://img.wesiedu.com/upload/9/a9/9a94fe2a637a3c46f1f86d79fa1ceff4.jpg)
![](http://img.wesiedu.com/upload/5/15/5156eca1c8edefd6a201c5290d8542cf.jpg)
![](http://img.wesiedu.com/upload/4/ab/4abb8a5fda664c9c26e2c01b23742585.jpg)
记
![](http://img.wesiedu.com/upload/2/4a/24aa56b958eb062b241100c9b120555f.jpg)
![](http://img.wesiedu.com/upload/3/5a/35a61e59371d3a7594ee15fa9e5f8e6e.jpg)
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