解题方法
1 . 已知双曲线
(
,
),实轴长为8,虚半轴长为
,
,
分别为双曲线左右焦点,点
,P为双曲线在第一象限上任意一点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b17a80dee44d744cf9ce671d4e8c0948.png)
A.![]() |
B.![]() |
C.若直线l交双曲线于A,B两点,且Q为![]() ![]() |
D.![]() ![]() |
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解题方法
2 . 已知函数
,
是大于0的常数.记曲线
在点
处的切线为
,
在
轴上的截距为
,
.
(1)当
,
时,求切线
的方程;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ad3da8a9798cf59dc08d553e342979e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d27c0ab3e2d7698f082854bafe4174dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2fe3251e054fe97089806ba7033f802.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc3423edf53e50f0b84c0a901f175f73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04cefacded707b7f8c9f8b9ade6ef32c.png)
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3卷引用:湖北省十一校2024届高三第一次联考数学试题
名校
解题方法
3 .
,
,当
时,
,则
的范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/673207f6b77b8192d25463d071737b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/818bc5ee1ba395ccbcbdea51b98f5c27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acf9f8bbbc66a74fabcbc0b99f22c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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6卷引用:湖北省十一校2024届高三第一次联考数学试题
湖北省十一校2024届高三第一次联考数学试题(已下线)第五讲:化归与转化思想【练】高三清北学霸150分晋级必备(已下线)第五章 一元函数的导数及其应用(压轴题专练,精选34题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第二册)(已下线)湖南省长沙市四县区2024届高三下学期3月调研考试数学试题变式题11-15(已下线)专题5 指数对数同构问题(过关集训)(压轴题大全)(已下线)第9题 构造函数利用单调性求参问题(压轴小题)
解题方法
4 . 已知双曲线
:
的实轴长为2,两渐近线的夹角为
.
(1)求双曲线
的方程:
(2)当
时,记双曲线
的左、右顶点分别为
,
,动直线
:
与双曲线
的右支交于
,
两点(异于
),直线
,
相交于点
,证明:点
在定直线上,并求出定直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6a46e678bf9d2df5ad4c782b3dc22f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c1dc3b2ca5b5e71f6f7acab671c8dc9.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/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
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4卷引用:湖北省荆门市2022-2023学年高二下学期期末数学试题
湖北省荆门市2022-2023学年高二下学期期末数学试题(已下线)专题3.5 直线与双曲线的位置关系【七大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)专题3-4 双曲线大题综合10种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)(已下线)第08讲:圆锥曲线(大题) (必刷7大考题+7大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)
5 . 已知椭圆E:
.若直线l:
与椭圆E交于A、B两点,交x轴于点F,点A,F,B在直线
:
上的射影依次为点D,K,G.
(1)若直线l交y轴于点T,且
,
,当m变化时,探究
的值是否为定值?若是,求出
的值;否则,说明理由;
(2)连接AG,BD,试探究当m变化时,直线AG与BD是否相交于定点?若是,请求出定点的坐标,并给予证明:否则,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d80b861ba40387cb2bcd04945f5a371a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd4cd13b1f570f617c7a409b08555079.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c778e409fe63e187a09444bc888e8f3.png)
(1)若直线l交y轴于点T,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f98e967a5ee2d3e7dbd7f1e62cf45b89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccb76e952369354a22ee4f1f43d87bb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
(2)连接AG,BD,试探究当m变化时,直线AG与BD是否相交于定点?若是,请求出定点的坐标,并给予证明:否则,说明理由.
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解题方法
6 . 若直线
与两曲线
、
分别交于
、
两点,且曲线
在
点处的切线为
,曲线
在
点处的切线为
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54b53b86bd516400d6fa7dabb3603f31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eae1b87c23b45ce5e5e74d5b1d73234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.存在![]() ![]() | B.当![]() ![]() |
C.![]() | D.![]() |
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5卷引用:湖北省荆门市2022-2023学年高二下学期期末数学试题
湖北省荆门市2022-2023学年高二下学期期末数学试题湖南师范大学附属中学2023届高三二模数学试题(已下线)重难点突破12 导数中的“距离”问题(七大题型)江苏省南京市2023-2024学年高二上学期期末模拟数学试题(已下线)专题10 切线问题(过关集训)
名校
解题方法
7 . 定义在R上的函数
和
满足
,且
,则下列不等式成立的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1ce3f01e2b6364f9a9fdaf197d5e29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b68e7272680b38b22e1271f550e3d7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29a0d4f26eb93dd01390581f996410c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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8 . 设函数
.
(1)当
时,讨论
的单调性;
(2)若
在
上单调递增,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8328a654a0750029a81d6dbe27575b3.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
9 . 若直线
与直线
是曲线
的两条切线,也是曲线
的两条切线,则
的值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b3c8be9aee074c9a3203abace248ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a5ad403fbc6d5e789b1ea26634a9ec7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12be206d66e65eb92ef08bad8cd8f71d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c7916024067055391593aca394764d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20f55da546b50231f2fd57c50459488.png)
A.![]() | B.0 | C.-1 | D.![]() |
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7卷引用:湖北省荆门市龙泉中学2023届高三5月模拟数学试题
湖北省荆门市龙泉中学2023届高三5月模拟数学试题辽宁省沈阳市2022届高三下学期二模数学试题(已下线)专题14 导数的概念与运算辽宁省大连市2022届高三第一次模拟考试数学试题(已下线)第39练 导数的概念、意义及运算(已下线)专题14 导数的概念与运算-3专题06导数的概念与几何意义
10 . 已知圆
:
,点
,
是圆
上任意一点,线段
的垂直平分线和半径
相交于点
.
(1)求动点
的轨迹
的方程;
(2)设直线
与(1)中的轨迹
相交于
、
两点,直线
、
、
的斜率分别为
、
、
(其中
),
的面积为
,以
、
为直径的圆的面积分别为
、
.若
、
、
恰好构成等比数列,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/553360f0476d7533adfae3d0e862946b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e3f7305f30d4d401a89e296d8a92ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ecd23dc68762cf5ba08eccdd52aa03c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531b3540af8141d06802fac03a04cbde.png)
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9卷引用:2015届湖北省荆门市高三元月调研考试理科数学试卷
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