2024·全国·模拟预测
名校
解题方法
1 . 在平面直角坐标系中,已知双曲线
的左、右焦点分别为
,过
且斜率为
的直线
与双曲线
的左、右两支分别交于
两点(
在第一象限),
的重心为
,内心为
,且
轴,则双曲线
的离心率为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d599cb4a589f90b0205f24c2e1fa021e.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47444b5fbc4252516d54263062e47c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e105760638b22b26ff8bec4354255e4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/039f7e8009ef18d707647ee256733c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
解题方法
2 . 已知
分别为双曲线
的左、右顶点,
为双曲线
上异于
的任意一点,直线
、
斜率乘积为
,焦距为
.
(1)求双曲线
的方程;
(2)设过
的直线与双曲线交于
,
两点(
不与
重合),记直线
,
的斜率为
,
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabd197d769d62408b492ab538eedd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.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/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2a72c6d7780757ab065fb29f47526.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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
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2024-01-13更新
|
1874次组卷
|
7卷引用:江西省上饶市北大邦实验学校2023-2024学年高二上学期期末质量检测数学试题
江西省上饶市北大邦实验学校2023-2024学年高二上学期期末质量检测数学试题吉林省白山市2024届高三一模数学试题河南省郑州市第十八中学2023-2024学年高二上学期期末模拟数学试题(六)(已下线)3.2.2 双曲线的简单几何性质【第三练】“上好三节课,做好三套题“高中数学素养晋级之路广东省广州市华南师大附中2024届高三上学期第二次调研数学试题(已下线)专题07 双曲线与抛物线(分层练)(五大题型+12道精选真题)(已下线)第四套 艺体生新高考全真模拟 (一模重组卷)
2024·全国·模拟预测
名校
解题方法
3 . 已知抛物线
的焦点为
,过
的直线与抛物线
交于A,B两点(点A在第一象限),若点D为抛物线
的准线上一点,且
,则直线
的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abac61d253f694e756215f5dc5ed6e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 已知数列
,若__________.
从下列三个条件中任选一个补充在上面的横线上,然后对题目进行求解.
①
;
②
,
,
(
,
);
③
,点
,
在斜率是2的直线上.
(1)求数列
的通项公式;
(2)求数列
的前
项和
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
从下列三个条件中任选一个补充在上面的横线上,然后对题目进行求解.
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0a3a3b9f5c56ee7d299127e5bb2e18.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a0d29f34218cd60cc6e9ce4dcd13925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a8bdde88872d024819dd2d3534237db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f093c61867ee4ce75f951d46b9b123.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0704f453b2de48d36911f7db496bbf82.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b065334d8f60c49f4bd3d9f1373fe4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/907f233ffca0f7a337dfa61f401e7bde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce36b768c1e1caac4f7b240c35dc4217.png)
(1)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83cf38189d5cbf627d2b82ac0eb76006.png)
(2)求数列
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c23f4855607b5b5754b6393507915de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1ae9a3b0b7aeb1545b65d91aa371b3c.png)
您最近一年使用:0次
5 . 已知抛物线
上三点
满足:
的重心是
,则直线
的斜率之和为 ______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc7ad3432ac96b0a38beaa7f2edc3499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ccc1567e0d5ddbf662022ba62d70b82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942e6dafcfcbf0682856b9f25178694d.png)
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名校
6 . 已知点
,
,点
在线段
上.
(1)求直线
的斜率;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67af31c17128c9d223dd468be103f2dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0026fa26c9cd07146ae610db57f6fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827539d066d1b78e7ef8bc1569864971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18f0281e6bbdbe08beeccb55adf84536.png)
您最近一年使用:0次
2023-06-11更新
|
560次组卷
|
6卷引用:江西省宁冈中学2022-2023学年高二下学期6月期末数学试题
江西省宁冈中学2022-2023学年高二下学期6月期末数学试题1.1.2 直线的倾斜角、斜率及其关系 课时练习-2022-2023学年高二上学期数学北师大版(2019)选择性必修第一册 (已下线)模块三 专题5 直线的倾斜角与斜率 A基础卷(已下线)模块三 专题8 直线的倾斜角与斜率 A基础卷广东省广州市一中2023-2024学年高二上学期10月月考数学试题(已下线)第01讲 2.1直线的倾斜角与斜率+2.2直线的方程+2.3直线的交点坐标与距离公式(原卷版)
名校
解题方法
7 .
中,角
所对的三边分别为
,若
的面积为1,则
的最小值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce187ecc91f879ee5ec46972663a2aef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.2 | B.3 | C.![]() | D.![]() |
您最近一年使用:0次
2022-09-10更新
|
1910次组卷
|
7卷引用:江西省吉安市第三中学2023届高三下学期3月月考数学(理)试题
解题方法
8 . 已知
为圆
:
上任意一点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e914add79b647716c0a108ccfd2c4ac5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f015ed8e497b4394053ddd19683a98f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b136e936c1006bd826ac544caf26bdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fc86c09d58cc8d1fe5f74eca2691a83.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
9 . 已知点A(2,-1),B(3,m),若
,则直线AB的倾斜角的取值范围为__________.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d4166de78a03ee38175d325c653dd9.png)
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2021-11-05更新
|
1022次组卷
|
8卷引用:江西省九江市永修县第一中学2022-2023学年高二上学期入学考试数学试题
江西省九江市永修县第一中学2022-2023学年高二上学期入学考试数学试题江西省鹰潭市贵溪市第一中学2023-2024学年高二上学期第一次月考数学试题山东省实验中学2021-2022学年高二10月月考数学试题新疆生产建设兵团第二师八一中学2021-2022学年高二上学期期中考试数学试题(已下线)2.1直线的倾斜角和斜率B卷沪教版(2020) 选修第一册 单元训练 第1章 直线的倾斜角与斜率(B卷)(已下线)第01讲 直线的方程 (精练)(已下线)第1章:直线与方程章末重点题型复习-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)
解题方法
10 . 已知实数x,y满足条件
,则
的取值范围为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82d5b033bbcef82b9757f3937483727c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61c708b574b555279880ea008b12bfaf.png)
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