解题方法
1 . 设双曲线C其中一支的焦点为F,另一支的顶点为A,其两渐近线分别为
. 若点B在m上,且
,则m与n的夹角的正切值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d754525eabcd1a0e45b9ffe11170ea50.png)
A.![]() | B.![]() | C.2 | D.![]() |
您最近一年使用:0次
2 . 直线与双曲线位置关系的判断
已知直线
,双曲线
,由
可得
①,
(1)当______ 时,①仅有一个解,此时直线与双曲线有一个交点;
(2)当
,若①对应的判别式为
,
当
时,①有两个不同的实数解,此时直线与双曲线有_____ 个交点;
当
时,①有两个相同的实数解,此时直线与双曲线有_____ 个交点;
当
时,①无解,此时直线与双曲线_____ 交点;
已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef66f4832adc43902055a7e6d258037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6d8b306e1df944fb248ca1456597d29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/505b27ac919667a0e94853d281c080a6.png)
(1)当
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf6139b2e744606ed95deb2126fbcbd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff35e4e3cdc188643c46265591575c6.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda1e6337ff7355c2fe9c19f9d619f5f.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c2b0eb6b8e515c616b5cdd4c37fefc3.png)
当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc39e3f9688bc77675ffdf0dd79da142.png)
您最近一年使用:0次
名校
3 . 清代青花瓷盖碗是中国传统茶文化的器物载体,具有“温润”“淡远”“清新”的特征.如图,已知碗体和碗盖的内部均近似为抛物线形状,碗盖深为
,碗盖口直径为
,碗体口直径为
,碗体深
,则盖上碗盖后,碗盖内部最高点到碗底的垂直距离为(碗和碗盖的厚度忽略不计)( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/976260cbf5e30856d4fd37a4b0a671a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b1fe1b971b780e443a9b13621611c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cdb26c5cdef6f16f4b39cd091041b439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e3cd64416baad4ebeceb2e9a94e55d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/9/cf2cba8c-6fd2-4067-8fba-1d61f779b398.png?resizew=125)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-06-06更新
|
1145次组卷
|
14卷引用:专题05 抛物线8种常见考法归类(2)
(已下线)专题05 抛物线8种常见考法归类(2)(已下线)专题13 抛物线的标准方程5种常见考法归类-【考点通关】2023-2024学年高二数学高频考点与解题策略(苏教版2019选择性必修第一册)河南省创新发展联盟大联考2023届高三预测数学(理科)试题2023届河南省创新发展联盟大联考仿真模拟预测数学(文科)试题第三章 圆锥曲线的方程 讲核心03(已下线)第23讲 抛物线及其标准方程5种常见考法归类-【暑假自学课】2023年新高二数学暑假精品课(人教A版2019选择性必修第一册)(已下线)第05讲 3.3.1抛物线及其标准方程(8类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)3.3 抛物线(精讲)-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)模块四 专题8 高考新题型(复杂情景题专训)基础夯实练(人教A)(已下线)第08讲 直线与圆锥曲线的位置关系(练习)(已下线)第十一章 数学建模(高三一轮)(已下线)专题08 抛物线的压轴题(5类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)(已下线)3.3.1 抛物线及其标准方程(5大题型)精讲-【题型分类归纳】2023-2024学年高二数学同步讲与练(人教A版2019选择性必修第一册)(已下线)专题26 抛物线及其标准方程5种常见考法归类 - 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
名校
4 . 中国国家大剧院是亚洲最大的剧院综合体,中国国家表演艺术的最高殿堂,中外文化交流的最大平台.大剧院的平面投影是椭圆
,其长轴长度约为
,短轴长度约为
.若直线
平行于长轴且
的中心到
的距离是
,则
被
截得的线段长度约为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/26/2ee257ff-b581-4a37-86fa-abaf5b28c6c5null?resizew=169)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a91e28d4bf7d04e4a79d1e120b05ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73bd8975741c7e768d21ee09a1f0de11.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74dee2e8849924124cbb31f9c6f15479.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-04-24更新
|
3167次组卷
|
5卷引用:江苏省决胜新高考2023届高三下学期4月大联考数学试题
解题方法
5 . 设平面直角坐标系中,双曲线
的左焦点为
,且与抛物线
有公共的焦点
.若
是
上的一点,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a3d3fefe175906355dda6ce8a0c4bd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c1ba86ffc6e5542b62319848c14acaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() |
您最近一年使用:0次
名校
解题方法
6 . 在平面直角坐标系
中,已知点
在抛物线
上,圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
,
为圆
上的动点,求线段
长度的最小值;
(2)若点
的纵坐标为4,过
的直线
与圆
相切,分别交抛物线
于
(异于点
),求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac8a3bffe545af2299cf999d44767206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/696194073d11052786104e11178adf2e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7551011cfb75b26f35b07d6617c6a18b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/280860dd039e1305a5ccc455f63e8223.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2022-12-11更新
|
544次组卷
|
3卷引用:江苏省G4联盟(苏州中学、扬州中学、盐城中学、常州中学)2022-2023学年高三上学期12月联考数学试题
7 . 在平面直角坐标系
中,已知点A,B在抛物线
:
上,抛物线C在A,B处的切线分别为
,
,且
,
交于点P.
(1)若点
,求
的长;
(2)从下面①②中选取一个作为条件,证明另外一个成立.
①直线AB过抛物线C的焦点;②点P在抛物线C的准线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.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/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec3fdb2722c0bcac5303546e87152a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)从下面①②中选取一个作为条件,证明另外一个成立.
①直线AB过抛物线C的焦点;②点P在抛物线C的准线上.
您最近一年使用:0次
8 . 已知
为坐标原点,抛物线
与曲线
的交于点
,其横坐标为
,记
平行于
的切线为
,
平行于
的切线为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310a72816188ba54fd532459517a3327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
A.![]() | B.![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
9 . 请在下面两题中选择一题作答:
题
设点
是抛物线
与双曲线
在第一象限的唯一公共点,点
,
分别是
的准线与
的两条渐近线的交点,则
的面积为__________ .
题
已知球的体积
和表面积
均是球半径
的函数,分别记为
,
若球
的半径
满足
,点
到球心
的距离为
,过点
作平面
,则平面
截球
所得截面圆的面积的最小值为__________ .
题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47a34029cc0f7665d32694f0837b2f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19cf08f835978859030ed7aceabafc27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ceea7e3117a7041ebe102193d087430b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
题
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508f5b0a8b1ac58f88d886a850f3ae1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be54e84508decfcce6d2fcbe6c8c1a92.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d524e6addf9435f64de5c45423b29b73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2816117b19e6c825c5131e136481c789.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5aeb128d36a0612d378b925c496df48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
10 . 已知
,
是过点
的两条互相垂直的直线,且
与椭圆
相交于A,B两点,
与椭圆
相交于C,D两点.
(1)求直线
的斜率k的取值范围;
(2)若线段
,
的中点分别为M,N,证明直线
经过一个定点,并求出此定点的坐标.
![](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/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae7b1b8a84ae7a1b2243b78cc932860d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2022-05-25更新
|
3761次组卷
|
13卷引用:江苏省泰州市兴化市2022届高三下学期5月模拟数学试题
江苏省泰州市兴化市2022届高三下学期5月模拟数学试题(已下线)3.1.2 椭圆的几何性质(2)(已下线)专题8 求定点定值运算(基础版)第三章 圆锥曲线的方程(B卷·能力提升练)-【单元测试】2022-2023学年高二数学分层训练AB卷(人教A版2019)(已下线)第3章 圆锥曲线与方程(A卷·知识通关练)(2)(已下线)专题31 圆锥曲线的垂直弦问题-1(已下线)考向36 圆锥曲线中的定点、定值问题(重点)(已下线)模块三 专题10 椭圆 A基础卷(已下线)模块三 专题13 椭圆 A基础卷3.1.2 椭圆的简单几何性质练习(已下线)第二章 圆锥曲线(单元基础检测卷)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)(已下线)模块一 专题2 《解析几何》单元检测篇 A基础卷(已下线)第04讲 拓展一:直线与椭圆的位置关系-【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)