(本题满分18分,其中第1小题5分,第2小题5分,第3小题8分)
在平面直角坐标系中,已知
![](https://img.yulucn.com/upload/7/e0/7e0d4ffc1ddb9e45a32aeb20f8d40755_thumb.jpg)
为坐标原点,点
![](https://img.yulucn.com/upload/9/3f/93f99a7c9983d906e46d4aca0a25a5e6_thumb.jpg)
的坐标为
![](https://img.yulucn.com/upload/a/11/a1106a62106877233ae93a1d08f79b20_thumb.jpg)
,点
![](https://img.yulucn.com/upload/e/69/e6956884d153b3978cfe8a5034d02dcd_thumb.jpg)
的坐标为
![](https://img.yulucn.com/upload/2/60/260b7e6b0550e0798c197d3b41c8de4f_thumb.jpg)
,其中
![](https://img.yulucn.com/upload/2/63/2639b55331bef2f99ac0bc6ec7a94341_thumb.jpg)
且
![](https://img.yulucn.com/upload/0/64/06466b1671b7daa150f6bd9d459752e7_thumb.jpg)
.设
![](https://img.yulucn.com/upload/7/d0/7d049e9f5605e60ea5314c40a7428d19_thumb.jpg)
.
(1)若
![](https://img.yulucn.com/upload/c/03/c0306e7a35ffed3ab766153d4cdee298_thumb.jpg)
,
![](https://img.yulucn.com/upload/a/6b/a6bc757c342d52adbeb9a3e48be4aded_thumb.jpg)
,
![](https://img.yulucn.com/upload/2/34/234c78578f12340a7a70ae7d1116d468_thumb.jpg)
,求方程
![](https://img.yulucn.com/upload/f/09/f095a5753839bf4117fa6cc6319de7e7_thumb.jpg)
在区间
![](https://img.yulucn.com/upload/2/a8/2a85760b989096b3519fa1ee45f0afd5_thumb.jpg)
内的解集;
(2)若点
![](https://img.yulucn.com/upload/9/3f/93f99a7c9983d906e46d4aca0a25a5e6_thumb.jpg)
是过点
![](https://img.yulucn.com/upload/b/bd/bbdebe5ce50c28bbb37a49b8876f042b_thumb.jpg)
且法向量为
![](https://img.yulucn.com/upload/8/80/880f170a3170e76ff7aea3e3a7d0eb4c_thumb.jpg)
的直线
![](https://img.yulucn.com/upload/d/b4/db4f980c8518f21d1d3bd86ae395952c_thumb.jpg)
上的动点.当
![](https://img.yulucn.com/upload/9/49/9499168ee0318ce81f85d92a7f463d55_thumb.jpg)
时,设函数
![](https://img.yulucn.com/upload/7/91/791d6d75f23d0846dba631a87ad7a8dd_thumb.jpg)
的值域为集合
![](https://img.yulucn.com/upload/0/ca/0caabe0fa100ce1ef5a2d5b2baa7bafc_thumb.jpg)
,不等式
![](https://img.yulucn.com/upload/a/d0/ad064a5223b79646c7fa1d25223fb2f6_thumb.jpg)
的解集为集合
![](https://img.yulucn.com/upload/9/d8/9d80b0369828f2472ce71bd37a35ae02_thumb.jpg)
. 若
![](https://img.yulucn.com/upload/6/26/626929a2c7a49e07f91b540103dfb6a3_thumb.jpg)
恒成立,求实数
![](https://img.yulucn.com/upload/b/ec/bec3a4cd9ebf39cb9f62ef29f33076b5_thumb.jpg)
的最大值;
(3)根据本题条件我们可以知道,函数
![](https://img.yulucn.com/upload/7/91/791d6d75f23d0846dba631a87ad7a8dd_thumb.jpg)
的性质取决于变量
![](https://img.yulucn.com/upload/8/47/8471522e2df1e6f5130693a73714d1d1_thumb.jpg)
、
![](https://img.yulucn.com/upload/7/c6/7c6185a0e3559dd0e7e0879fc8b7c1eb_thumb.jpg)
和
![](https://img.yulucn.com/upload/e/84/e84365dccd3808e411276ca64df8eb2e_thumb.jpg)
的值. 当
![](https://img.yulucn.com/upload/9/49/9499168ee0318ce81f85d92a7f463d55_thumb.jpg)
时,试写出一个条件,使得函数
![](https://img.yulucn.com/upload/7/91/791d6d75f23d0846dba631a87ad7a8dd_thumb.jpg)
满足“图像关于点
![](https://img.yulucn.com/upload/b/10/b10fc286538cebad882f6b2e2ad3416b_thumb.jpg)
对称,且在
![](https://img.yulucn.com/upload/c/52/c52fd94899c44860f3bac93bd0254d0e_thumb.jpg)
处
![](https://img.yulucn.com/upload/7/91/791d6d75f23d0846dba631a87ad7a8dd_thumb.jpg)
取得最小值”.(说明:请写出你的分析过程.本小题将根据你对问题探究的完整性和在研究过程中所体现的思维层次,给予不同的评分.)