名校
解题方法
1 . 如图1,直线
与x轴,y轴分别相交于A,B两点,将
绕点O逆时针旋转90°得到
,过点A,B,D的抛物线
叫做l的关联抛物线,而直线l叫做
的关联直线.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
,则抛物线
表示的函数解析式为________;若抛物线
,则直线l表示的函数解析式为______.
(2)求抛物线
的对称轴(用含m,n的代数式表示);
(3)如图2,若直线
,抛物线
的对称轴与
相交于点E,点F在l上,点Q在抛物线
的对称轴上.当以点C,E,Q,F为顶点的四边形是以
为一边的平行四边形时,求点Q的坐标;
(4)如图3,若直线
,G为
中点,H为
中点,连接
,M为
中点,连接
.若
,求直线l,抛物线
表示的函数解析式.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a88699a9cab3fb5e061e722d1f60a8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a9a6eeeebf3cff569578d7366b755aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/9/ef9d3ce4-d4b1-4552-a814-082583273cf8.png?resizew=458)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90717234dbf965e8cb5f8fe2e53776da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef60818f89bebb4ed87db774a5149fd9.png)
(2)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
(3)如图2,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ec899da04f19dca04bba10ffc4358a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
(4)如图3,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163a3df8d98950645d7a249141b679d.png)
![](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/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc91a53e2534ce7034372b0add103eac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c27eda162792128da25f541303a3088.png)
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名校
2 . 如图,在平面直角坐标系
中,过
外一点
引它的两条切线,切点分别为
,若![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f798964a881ea48b2c79b7fd96ebd7.png)
,则称
为
的环绕点.
![](https://img.xkw.com/dksih/QBM/2021/8/2/2777681467408384/2782948712816640/STEM/0826976a-b1f6-4b0f-b7d9-ac20165ed90b.png?resizew=259)
(1)当
O半径为1时,
①在
中,
的环绕点是__________.
②直线
与
轴交于点
,与
轴交于点
,若线段
上存在
的环绕点,求
的取值范围;
(2)
的半径为1,圆心为
,以
为圆心,
为半径的所有圆构成图形
,若在图形
上存在
的环绕点,直接写出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08f798964a881ea48b2c79b7fd96ebd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b685bc5ff8d47424c0d4f2f8c08e58bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://img.xkw.com/dksih/QBM/2021/8/2/2777681467408384/2782948712816640/STEM/0826976a-b1f6-4b0f-b7d9-ac20165ed90b.png?resizew=259)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091e86ca89e484b331fd90125a5e5af3.png)
①在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5f4280e5155144bc68b74ecd9e3de45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
②直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bebb3b7f47e0decd48e64cb32aaa5903.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091e86ca89e484b331fd90125a5e5af3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/180735d52856f4393e40e28e7fcc95bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c013c86ffcabc839b93c5725519c7fe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c00653a92e7962ecc3a9cc1a4a49e8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9347ab0d001ed7e8f51f9886ce88ac64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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3 . 奔驰定理:已知
是
内的一点,
,
,
的面积分别为
,
,
,则
.“奔驰定理”是平面向量中一个非常优美的结论,因为这个定理对应的图形与“奔驰”轿车(Mercedes benz)的logo很相似,故形象地称其为“奔驰定理”若
是锐角
内的一点,
,
,
是
的三个内角,且点
满足
,则必有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4962343ca7d065aee473dbf79eb8d3c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3304bc1372275307dce0bf4e98b8f3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2319b6a5373bc8eb13772b8e6d047779.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ea3c7cd2f23b4521e64a7e64844ec48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/089e8a7f6c535fc3cd270af428d55f65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9659621d48404d8e5479cbab9050e5a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec09a159d6760fca8ae5966bf97b4e49.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() |
您最近一年使用:0次
2019-12-04更新
|
2810次组卷
|
5卷引用:河南省南阳市2019-2020学年高三上学期期中数学(理)试题
河南省南阳市2019-2020学年高三上学期期中数学(理)试题湖南省邵阳市武冈市2021-2022学年高一下学期期中数学试题(已下线)平面向量专题:奔驰定理解三角形面积比值问题-【题型分类归纳】2022-2023学年高一数学同步讲与练(人教A版2019必修第二册)(已下线)第五篇 向量与几何 专题13 奔驰定理 微点2 奔驰定理(二)(已下线)专题突破卷15 三角形的“四心”及奔驰定理
名校
4 . 已知点P和非零实数
,若两条不同的直线
均过点P,且斜率之积为
,则称直线
是一组“
共轭线对”,如直
是一组“
共轭线对”,其中O是坐标原点.
是一组“
共轭线对”,求
的夹角的最小值;
(2)已知点A(0,1)、点
和点C(1,0)分别是三条直线PQ,QR,RP上的点(A,B,C与P,Q,R均不重合),且直线PR,PQ是“
共轭线对”,直线QP,QR是“
共轭线对”,直线RP,RQ是“
共轭线对”,求点P的坐标;
(3)已知点
,直线
是“
共轭线对”,当
的斜率变化时,求原点O到直线
的距离之积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5883f18fe46765e94aba381bff58d501.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120be1fe068d0caeb470903565101d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf497f6e2c8534203fd6c147451d35e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af379ba5a9cf6cab6815c3252ce23beb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
(2)已知点A(0,1)、点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46c85c66ab0b89e84a10aad864251771.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d85d8c1f8add55bdc8c393be3ba2ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0009bbfff99038d2af22c753b87136dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757b384946bb1b4ff9b754ee6aa7f4d3.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70991c59719c9c37e186a7bc8a121ca2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4401491646ca39b6376c31f1f515b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd8f64ebec4a71a609204458cc54df82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc4fb814dbdd5dc584a06be40da14146.png)
您最近一年使用:0次
2018-12-05更新
|
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5卷引用:【全国百强校】上海市复旦附中2018-2019学年高二上学期期中考试数学试题
【全国百强校】上海市复旦附中2018-2019学年高二上学期期中考试数学试题上海市上海师范大学附属中学2020-2021学年高二上学期期中数学试题上海市青浦高级中学2020-2021学年高二上学期期中数学试题上海市建平中学2022-2023学年高一下学期期末数学试题(已下线)2.1 直线的倾斜角与斜率-2021-2022学年高二数学尖子生同步培优题典(人教A版2019选择性必修第一册)