1 . 已知以下事实:反比例函数
(
)的图象是双曲线,两条坐标轴是其两条渐近线.
(1)(ⅰ)直接写出函数
的图象
的实轴长;
(ⅱ)将曲线
绕原点顺时针转
,得到曲线
,直接写出曲线
的方程.
(2)已知点
是曲线
的左顶点.圆
:
(
)与直线
:
交于
、
两点,直线
、
分别与双曲线
交于
、
两点.试问:点A到直线
的距离是否存在最大值?若存在,求出此最大值以及此时
的值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07854693dd2e33f66030d6106eb6e0ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)(ⅰ)直接写出函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c190daf6e3d1cdd5019c3f50a4f842e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
(ⅱ)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9a7e0e5238148676a584b1748e04d3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ff2f5d89e535bab877ad226f086742a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
2024-03-21更新
|
1479次组卷
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5卷引用:湖南省衡阳市第八中学2024届高三下学期高考适应性练习卷(三)数学试题
2 . 已知双曲线E:
(
,
)一个顶点为
,直线l过点
交双曲线右支于M,N两点,记
,
,
的面积分别为S,
,
.当l与x轴垂直时,
的值为
.
(1)求双曲线E的标准方程;
(2)若l交y轴于点P,
,
,求证:
为定值;
(3)在(2)的条件下,若
,当
时,求实数m的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/681ab02a01fa41c784b688575fe90539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b74110bc818c2f5a53d63451c5251eb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/436a2732e9c9d5ce401c448cd9de80e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b72cb228a0747bf4b779cc337749a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d3a5255a0a61f4d297874ecd1967b01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b690956d61cb5a9f955a87093856eb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfc2628ebeec39f2ff82e216e780e3c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9cdbc51da77d74d60ef8e2878fa2dea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac8a4086cd8af00e89c57fdfd905114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd72016a9855cbf0056ff732fe872612.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ac8a4086cd8af00e89c57fdfd905114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fa84eb397ffcbbf3a26d95e50f0e7db.png)
(1)求双曲线E的标准方程;
(2)若l交y轴于点P,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8f34c9aba5a3834c8d2c76701366c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccee36f0ebe053f4bd976b31aab0efa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff141a77e796894f84d0104f8f947e8a.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165e3984c374e63ff90022b333efa103.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a11319d09d138b1ecc48692209ceec.png)
您最近一年使用:0次
2022-10-25更新
|
2083次组卷
|
5卷引用:湖南省“一起考”大联考2023-2024学年高三下学期模拟考试数学试题(一)
名校
3 . 已知点
,
,点A满足
,点A的轨迹为曲线C.
(1)求曲线C的方程;
(2)若直线
与双曲线:
交于M,N两点,且
(O为坐标原点),求点A到直线l距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2e56502edba9511c1ce84ecbf6d2e99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8d89e9d012179b974e2c6bb481fa07b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17b8dfe216ef4fed64026f3bf694cc23.png)
(1)求曲线C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14f8ae565db8a7d4b95fdd85e28afa2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4489ea382b7a51cd5fc8c5ae585a3ec4.png)
您最近一年使用:0次
2022-04-08更新
|
1961次组卷
|
5卷引用:湖南省部分学校2024届高三下学期一起考大联考模拟(二)数学试题