解题方法
1 . 已知双曲线C:
的离心率为
,点
在双曲线上.
(1)求双曲线C的方程;
(2)若A,B为双曲线的左、右顶点,
,若MA与C的另一交点为P,MB与C的另一交点为Q(P与A,Q与B均不重合)求证:直线PQ过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f12044661d15a805a90206c16f6e8a7d.png)
(1)求双曲线C的方程;
(2)若A,B为双曲线的左、右顶点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fb95c0dbba2ce77a7dcc42fa06e058.png)
您最近一年使用:0次
2023-03-11更新
|
518次组卷
|
3卷引用:山西省晋中市2023届二模数学试题(B卷)
解题方法
2 . 已知抛物线
:
过点
.
(1)求抛物线
的方程;
(2)
,
是抛物线
上的两个动点,直线
的斜率与直线
的斜率之和为4,证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86a6be776cdd229e5c1339265b23624a.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](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/c5db41a1f31d6baee7c69990811edb9f.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/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
2023-09-05更新
|
1039次组卷
|
5卷引用:山西省吕梁市2023届高三二模数学试题
山西省吕梁市2023届高三二模数学试题(已下线)考点巩固卷22 抛物线方程及其性质(十大考点)(已下线)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员(已下线)第06讲 拓展三:直线与抛物线的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)3.3.1 抛物线的标准方程(五大题型)-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)
3 . 已知双曲线
经过点
,直线
、
分别是双曲线
的渐近线,过
分别作
和
的平行线
和
,直线
交
轴于点
,直线
交
轴于点
,且
(
是坐标原点)
(1)求双曲线
的方程;
(2)设
、
分别是双曲线
的左、右顶点,过右焦点
的直线交双曲线
于
、
两个不同点,直线
与
相交于点
,证明:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62a4ba61e0fe0cb463581292835301f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87f385409ff4e9b458fc4c22d4561243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e0bd0b8ce573a569e224ff647d7806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87f385409ff4e9b458fc4c22d4561243.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82e0bd0b8ce573a569e224ff647d7806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893b9b7b7360afaf5924b8e32d00dee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2023-04-21更新
|
810次组卷
|
4卷引用:山西省太原市、大同市2023届高三二模数学试题
山西省太原市、大同市2023届高三二模数学试题山西省阳泉市2023届高三二模数学试题(已下线)第五篇 向量与几何 专题4 极点与极线 微点4 极点与极线问题常见模型总结(二)(已下线)专题8.3 双曲线综合【九大题型】(举一反三)(新高考专用)-2
解题方法
4 . 已知函数
,其中a为常数,e为自然对数底数,
…,若函数
有两个极值点
,
.
(1)求实数a的取值范围;
(2)证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87fac1e5eab0a126007a2213ee3b6a06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c07d7af2ede4abfa4d647b4058992d00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c814128ea2139e33db94ea590e7c2223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aec19b68e3add9d5bfcc6269a1855b87.png)
(1)求实数a的取值范围;
(2)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eeb7c63c22dc5e9ae9b17a693af2424c.png)
您最近一年使用:0次
2023-04-20更新
|
816次组卷
|
5卷引用:山西省阳泉市2023届高三三模数学试题
山西省阳泉市2023届高三三模数学试题广西南宁市2023届高三二模数学(理)试题(已下线)专题04函数与导数(解答题)(已下线)第三章 重点专攻三 函数零点问题(讲)(已下线)模块三 大招16 极值点&拐点偏移
名校
解题方法
5 . 已知双曲线C:
(
,
)的焦距为
,离心率
.
(1)求双曲线C的方程;
(2)设P,Q为双曲线C上异于点
的两动点,记直线MP,MQ的斜率分别为
,
,若
,求证:直线PQ过定点.
![](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/790f682ab3b50ba3f79e1ab6c67c75a5.png)
(1)求双曲线C的方程;
(2)设P,Q为双曲线C上异于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e05007098be2ef2769bb3c83d68ea3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe91cc3bfc93ef1cc3369fa6756bbd4d.png)
您最近一年使用:0次
2023-04-09更新
|
1094次组卷
|
6卷引用:山西省吕梁市柳林县鑫飞中学2023-2024学年高三上学期学情调研质量检测数学模拟试卷
名校
解题方法
6 . 已知椭圆
:
,设过点
的直线
交椭圆
于
,
两点,交直线
于点
,点
为直线
上不同于点A的任意一点.
,求
的取值范围;
(2)若
,记直线
,
,
的斜率分别为
,
,
,问是否存在
,
,
的某种排列
,
,
(其中
,使得
,
,
成等差数列或等比数列?若存在,写出结论,并加以证明;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40c1fb9f8b59508b1b58180c899d1787.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c93d5f956a50f96f2b257a61bcd1db09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b46c607b3deac746c0ef3389ad8f65c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c4c865445dda4a59b6d5cb18fd74404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc03cd251a03b73ebae3ea1d6bca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2eb8885dc1f43959efc27d89291c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84ad6ffc62173c68ff3ca5cf19f14b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5cfbf857a2ac07cbdada127302a3a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8cc03cd251a03b73ebae3ea1d6bca76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2eb8885dc1f43959efc27d89291c61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b84ad6ffc62173c68ff3ca5cf19f14b9.png)
您最近一年使用:0次
2023-03-18更新
|
1531次组卷
|
4卷引用:山西省2023届高三适应性考试数学试题
名校
解题方法
7 . 已知函数
.
(1)若不等式
在
上恒成立,求实数a的取值范围;
(2)若
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1eb6713f45458fd1b47b9fa64ea0157.png)
(1)若不等式
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e9c599e8d420006448905acec2b8234.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac4cbc7b067862a3d9c6789b392fc068.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2eba41c708a8c48e40f54b619eb5cb02.png)
您最近一年使用:0次
2023-03-10更新
|
1217次组卷
|
7卷引用:山西省部分学校2023届高三下学期质量检测试题
山西省部分学校2023届高三下学期质量检测试题北京市第五十七中学2022-2023学年高二下学期3月月考数学试题湖北省新高考联考协作体2022-2023学年高三下学期4月月考数学试题安徽省江南十校2022-2023学年高二下学期5月联考数学模拟试题(已下线)拓展十:利用导数研究不等式恒(能)成立问题5种考法总结-【帮课堂】2022-2023学年高二数学同步精品讲义(人教A版2019选择性必修第二册)(已下线)专题2 导数(5)(已下线)模块一 专题5 导数及其应用 2 (北师大2019版)
名校
解题方法
8 . 已知点
为双曲线
上一点,
的左焦点
到一条渐近线的距离为
.
(1)求双曲线
的标准方程;
(2)不过点
的直线
与双曲线
交于
两点,若直线PA,PB的斜率和为1,证明:直线
过定点,并求该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00d5d8cc31aaca7fc2eafb99eac7629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)不过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
您最近一年使用:0次
2023-07-20更新
|
1350次组卷
|
10卷引用:山西省运城市运城中学2023届高三第二次模拟数学试题
山西省运城市运城中学2023届高三第二次模拟数学试题河北省张家口市2023届高三三模数学试题(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)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)(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)专题11 平面解析几何-4(已下线)专题15 圆锥曲线综合(已下线)3.2.2 双曲线的几何性质(2)(已下线)微考点6-6 圆锥曲线中斜率和积与韦达定理的应用
9 . 已知函数
.
(1)若函数
在区间
上恰有两个极值点,求a的取值范围;
(2)证明:当
时,在
上,
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91af7006414826041eada8d63b3afcf5.png)
(1)若函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01dc2d99655cf7598837cb0886166ed.png)
(2)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f26a6ffed5c91ce744a2be8ca57159.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/870ebc2f7aabb028024894568d749934.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1501063eeb493e8919f16f9bba4a3567.png)
您最近一年使用:0次
2023-05-19更新
|
269次组卷
|
2卷引用:山西省大同市2023届高三下学期5月质量检测数学试题
名校
10 . 已知函数
为函数
的导函数.
(1)讨论函数
的单调性;
(2)已知函数
,存在
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f389a23b0a635912915e241af34fa9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(1)讨论函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
(2)已知函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38beb343561c01c2d4210e512d5e95df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8c894ca33d1f108f9f5a19f6a6c6c95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c7847abd5a830ff448f260b5107ac52.png)
您最近一年使用:0次
2023-06-14更新
|
950次组卷
|
7卷引用:山西省运城市运城中学2023届高三第二次模拟数学试题
山西省运城市运城中学2023届高三第二次模拟数学试题安徽省六安第一中学2023届高考适应性考试数学试题河北省张家口市2023届高三三模数学试题(已下线)专题12 导数及其应用(已下线)专题19 导数综合-1吉林省延边州2024届高三下学期教学质量检测一模数学试题(已下线)第五章 导数及其应用 (压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第二册)