名校
解题方法
1 . 已知双曲线
的左、右焦点分别为
,过
作直线l垂直于双曲线的一条渐近线,直线l与双曲线的两条渐近线分别交于A,B两点,若
,且
,则双曲线C的离心率
的取值范围为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.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/ff38c403c8dcb89a35898ba41355e535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fce598e15f7e987f25457f07c817c4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
您最近一年使用:0次
2021-07-26更新
|
2663次组卷
|
10卷引用:重庆市第一中学2021届高三下学期第二次月考数学试题
重庆市第一中学2021届高三下学期第二次月考数学试题(已下线)3.2 双曲线(难点)(课堂培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)(已下线)10.3 平面向量的应用(精练)-【一隅三反】2022年高考数学一轮复习(新高考地区专用)(已下线)试卷09(第1章-3.2双曲线)-2021-2022学年高二数学易错题、精典题滚动训练(苏教版2019选择性必修第一册)(已下线)专题05 平面解析几何(选择题、填空题)-备战2022年高考数学(理)母题题源解密(全国甲卷)(已下线)2020年高考江苏数学高考真题变式题6-10题(已下线)解密15 双曲线方程(分层训练)-【高频考点解密】2022年高考数学二轮复习讲义+分层训练(新高考专用)(已下线)专题25 圆锥曲线压轴小题必刷100题-【千题百练】2022年新高考数学高频考点+题型专项千题百练(新高考适用)新疆乌鲁木齐八一中学2022-2023学年高二上学期第一次月考数学试题广西百色市平果市铝城中学2023-2024学年高二下学期3月份测试数学试卷
解题方法
2 . 设
,
为单位向量,则
的最大值是________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb80eb942aafb194fadc473776f35b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/433b94c39737727e53468df419d8314a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb6fa8154c19843067718d676820c4b2.png)
您最近一年使用:0次
3 . 已知抛物线
:
的焦点为
,
是抛物线
上一点,且满足
.
(1)求抛物线
的方程;
(2)已知直线
与抛物线
交于
,
两点,且
,线段
的中点
在直线
上.
(i)求直线
的方程;
(ii)证明:
,
,
成等差数列,并求该数列的公差.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86bf50587d7523b621c9758b11d52400.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知直线
![](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/1e29f0900164e8ff6af514a46c8b5017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
(i)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(ii)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db36eb152e1ee9a6c138b30ad2ced0aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b32d93c0a0af14ab72fb284ce23c0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a356309ceefe2eaae58871c32c182e4.png)
您最近一年使用:0次
解题方法
4 . 设
,
,
,
是两两不同的四个点,若
,
,且
,则称
,
调和分割
,
.现已知平面上两点C,D调和分割A,B,则下列说法正确的是( )
![](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/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c8bcc8dee6f13f12cf31c13d7e5e722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa211f915e67bdc41fda5ac8e672429.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e2e34fee0d65efbeb5ec9a53b6a848f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b56e44e4f0424a2b7a45567120a2e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e47cd514b2920609e3781c87df6ab70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
A.点C可能是线段![]() |
B.点D不可能是线段![]() |
C.点C,D可能同时在线段![]() |
D.点C,D不可能同时在线段![]() |
您最近一年使用:0次
名校
5 . 已知O为坐标原点,对于函数
,称向量
为函数
的伴随向量.
(1)设函数
,试求
的伴随向量
;
(2)由(1)中函数
的图象(纵坐标不变)横坐标伸长为原来的2倍,再把整个图象向右平移
个单位长度得到
的图象,已知
,
,问在
的图象上是否存在一点
,使得
.若存在,求出
点坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc54bc56c16baa3643686b85a6130e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074d049ba730bc0a038a076d5eb10035.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
(1)设函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1577d749fd6363a3d864dbbae1fbc6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b6799b234237333b0efa331d98f0374.png)
(2)由(1)中函数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f785147690f83dcee0a0bc6c327e75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a813b5adbf5c7082561237894ba6d599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0c21dde2ad1e31c337bfb78c810ccb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aab5da44c04986fec56fe0429e7bd38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f786a5701dc1a8a015e8843c3360151b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b354aefbabbc26c70388d76919dad557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2021-03-31更新
|
298次组卷
|
3卷引用:江苏省常州市“教学研究合作联盟”2020-2021学年高一下学期3月阶段调研数学试题
名校
6 . 借助三角函数定义及向量知识,可以方便地讨论平面上点及图象的旋转问题.试解答下列问题.
(1)在直角坐标系中,点
,将点
绕坐标原点
按逆时针方向旋转
到点
,如果终边经过点
的角记为
,那么终边经过点
的角记为
.试用三角函数定义,求点
的坐标;
(2)如图,设向量
,把向量
按逆时针方向旋转
角得向量
,试用h、k、θ表示向量
的坐标;
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c795a170-83f8-4bb9-a7f1-b86b0144183b.png?resizew=98)
(3)设
、
为不重合的两定点,将点B绕点A按逆时针方向旋转
角得点C.判断C是不能够落在直线
上,若能,请求出θ的三角函数值(正弦、余弦、正切不限),若不能,说明理由.
(1)在直角坐标系中,点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675de67c4df38e172f7de40b03508fb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c67d01e61dc0042e67b5e8ec8e727c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3982ebdedf29c3890e6e891263bfbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(2)如图,设向量
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550d5fb27e50cbe46bc1586be89cab8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9795e7f5cb9b366776c41d8f3f43942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be64d59ac6538a0f4d79fb825e082081.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/12/c795a170-83f8-4bb9-a7f1-b86b0144183b.png?resizew=98)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bdb225f362f150791f7483a96a18d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72babdedbe6b32b150cc3ee258a7c310.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
您最近一年使用:0次
2021-07-24更新
|
490次组卷
|
6卷引用:上海市复旦大学附属中学2019-2020学年高一下学期期末数学试题
上海市复旦大学附属中学2019-2020学年高一下学期期末数学试题6.2.1两角和与差正弦、余弦、正切公式(作业)-【上好课】2020-2021学年高一数学下册同步备课系列(沪教版2020必修第二册)北京市一六六中学2020-2021学年高一下学期期中考试数学试题(已下线)上海期末真题精选50题(大题压轴版)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)(已下线)第6章 三角(章节压轴题解题思路分析)-2020-2021学年高一数学下册期中期末考试高分直通车(沪教版2020必修第二册)1.2向量的加法运算
7 . △QAB是边长为6的正三角形,点C满足
,且
,
,
,则
的取值范围是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1ebaa8302725f01b32120004bf4fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de8610232c77741a37463feba1a66c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc5b4357fd97fc6a2328953fe45a294.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310c2f1bd375cda66c1180f465f49f47.png)
您最近一年使用:0次
2021-01-15更新
|
714次组卷
|
2卷引用:河南省驻马店市新蔡县2020-2021学年高三上学期四校联考理数试题
名校
解题方法
8 . 如图,在等腰直角三角形ABC中,
,
,以AB为直径在
外作半圆O,P是半圆弧AB上的动点,点Q在斜边BC上,若
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcd0ced286a0fbc7e4862f8147264277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c8a189a2dcf173188c7ec1ac41cae3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78ce7fb8c9f05610966cc356a3f97779.png)
您最近一年使用:0次
2020-03-05更新
|
1401次组卷
|
4卷引用:山东省聊城市莘县第一中学2018-2019学年高一下学期期末数学试题
山东省聊城市莘县第一中学2018-2019学年高一下学期期末数学试题(已下线)专题03 “三法”解决平面向量数量积问题(第二篇)-2020高考数学压轴题命题区间探究与突破(已下线)第08讲 平面向量的正交分解及坐标表示福建师范大学附属中学2023-2024学年高一下学期期中考试数学试卷
名校
9 . 平面直角坐标系xOy内,点
,动点
和Q关于原点O对称,
,
.
(1)以原点O和点A为顶点作等腰直角三角形ABO,使
,求向量
坐标;
(2)若
且P、M、A三点共线,求
的最小值;
(3)若
,且
,
,求直线AQ的解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8293156150e4eb50a1bdd71090917dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
(1)以原点O和点A为顶点作等腰直角三角形ABO,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96d9e134e1820d80612be1bc590993e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/329fdf7d989f77a32ca9e0361a9cc956.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/881a9727fa891bd80ac7c64abb0518ab.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea9703534eceb8ccbfebb7a4510d5530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98bbff91df26858f512a572c81907716.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36753c437b2799a0afa028ae919f8b4c.png)
您最近一年使用:0次
名校
10 . 如图,点
是半径为1的扇形圆弧
上一点,
,
,若
,则
的最小值是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/67065b54-3ed7-441e-abb2-b9462fe44a72.png?resizew=134)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f72452cc769db86489edfd6bd0ec45fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba022811a0e9ecb5c033eb7ab92efd0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02ce85657e854d01988bfb612238b47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/1/67065b54-3ed7-441e-abb2-b9462fe44a72.png?resizew=134)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次