解题方法
1 . 已知圆
过点
、
、
,
为圆
上的动点,点
,
,O为坐标原点,
,
分别为线段
,
的中点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5dffbdc6dc7c0479261716cddd2c3f26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/110d3e40e0fbb017ec72c3d9923ae624.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abde190b86cd95b7983ba822cdeaea62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/169d67447772c5485894d82d0a0d68e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5815cc29f60d2aa538c4dd30e0803a4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd05f27fb25e486092d776339fe3b942.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80be8bad2b64e0297363ba555751a259.png)
A.![]() |
B.![]() |
C.![]() |
D.![]() ![]() |
您最近一年使用:0次
解题方法
2 . 已知抛物线
的焦点为
,其准线与
轴的交点为
.直线
与
没有公共点,直线
经过点
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fa2c731aaa4005382d5b4324e29fbb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/6ed4c118054df599726d1351465645ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a388a8e291afb1c37d0faee69dee2a.png)
A.![]() | B.![]() ![]() |
C.以![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
2023高二·全国·专题练习
3 . 平面向量的数量积
(1)定义:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
_______ ,规定![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ef1e9487f2ebf383dcc471740e501b.png)
_______ ;
(2)坐标表示:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
_______ ,其中
;
(3)运算律
①交换律:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
_______ ;②结合律![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6f27d6d41bc568190a033cfc60c0c3.png)
_______ ;③数乘:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0811e6cc59bc526605b7a8f69c85fe.png)
_______ .
(4)
在
方向上的投影是_______ ;
(5)
的几何意义:数量积
等于
的模
与
在
的方向上的投影的乘积.
(1)定义:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3ef1e9487f2ebf383dcc471740e501b.png)
(2)坐标表示:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67c9854341c5afb27815f669c1d8594e.png)
(3)运算律
①交换律:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c6f27d6d41bc568190a033cfc60c0c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da0811e6cc59bc526605b7a8f69c85fe.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
(5)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba3c6bd21d9c27a68b970f446f04d6df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/854e16eb319ee454088f5b527cf6c4d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6fbff85947f4df50ae1b17e967a158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b45ba716f03748c19b7ce2f99af536ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c5562bd4d1b54424330cb6329cd79d.png)
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4 . 已知向量
,满足
的动点
的轨迹为
,经过点
的直线
与
有且只有一个公共点
,点
在圆
上,则
的最小值为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d3090783e0a6f5ef455736e136c2037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7dced91de1b8c38aa95ffee0e5dc202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4b2bb30137f92479d11827ee769f001.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfbe851b6d4ea47349cf2f3525b8f797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
A.![]() | B.![]() |
C.![]() | D.1 |
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2022·上海浦东新·模拟预测
名校
解题方法
5 . 已知
,函数
的图象为曲线
.
、
是
上的两点,
在第一象限,
在第二象限.设点
、
.
(1)若
到
和到直线
的距离相等,求
的值;
(2)已知
,证明:
为定值,并求出此定值(用
表示);
(3)设
,且直线
、
的斜率之和为
.求原点
到直线
距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d6eb8e22b38b1a1f2f4550bc8633bd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/4bcd8ee2d8367c167d6ae0abc741b6b8.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/7ae4f082771efb99874041fe9c32aa81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f02e22b0fc087bd2cbb96ec3483b58e8.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79e1023c4d2941e4753560787b7a9851.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ace585d3cc2e113a0927cdf9e56756a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1010846eeec6c9da29640f5aa3f8738.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7acff98078cdd32804d8f1c4efbe2ddd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆C的短轴长与长轴长之比为
,焦点坐标分别为
,
.
(1)求椭圆C的标准方程;
(2)已知
,
,P是椭圆C上异于A、B的任意一点,直线AP、BP分别交y轴于M、N,求
的值;
(3)在(2)的条件下,若
,
,且
,
,分别以OG、OH为边作两正方形,求此两正方形的面积和的最小值,并求出取得最小值时的G、H点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
(1)求椭圆C的标准方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297bc912cb09546db07e4fb6be67af40.png)
(3)在(2)的条件下,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138775330e7da4ab35d57671e5b0596b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7daa3997288d0f4eefce24d77359770f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20e65c2010af65032354ecf1f5982ae2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1035aef67a1a6faf561f5cc0cebf87f.png)
您最近一年使用:0次
2021高二·江苏·专题练习
7 . 已知点
且
点
点M在点N的左面
是直线
上的两个动点且
,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479b59c982458a539f9cb30a8a115ceb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff7df203570c1c0cab44363d4b704189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1095697f15f380923771f92a7890a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d532ce76942846df88c6f66112e50f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6915db62bfca9bb78145d1cc3a6125ae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/226b1ffc3c6d23ae6c79a4626a727289.png)
您最近一年使用:0次
名校
解题方法
8 . 如图,已知
,
,
,直线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/d24df8f1-3e2d-4ea5-ac81-d7b48ced6ead.png?resizew=143)
(1)求直线l经过的定点坐标;
(2)若直线l等分
的面积,求直线l的方程;
(3)若
,点E、F分别在线段BC和AC上,上
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1dbb7313d3364656e5daef5ff5f219f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87baa7770b063bfe7cd8f8fce57d9181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1db6a960cda734e2185a736b7506d8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93b037e6b696e6bbbe3bdfeb540553d9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/16/d24df8f1-3e2d-4ea5-ac81-d7b48ced6ead.png?resizew=143)
(1)求直线l经过的定点坐标;
(2)若直线l等分
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16bf7dae3f8a49fe804fa2deba23b37d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c45ab82dfb318518afeb5df15e48696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5514a14f65f15ecf4078f201403df438.png)
您最近一年使用:0次
2021-11-19更新
|
406次组卷
|
4卷引用:附加篇:直线与方程(向量法)
(已下线)附加篇:直线与方程(向量法)上海市徐汇区西南位育中学2019-2020学年高二上学期期中数学试题(已下线)第1章 直线与方程 单元综合检测(难点)上海市青浦高级中学2022-2023学年高二上学期9月月考数学试题
名校
9 . 已知线段
的端点
,端点
在圆
上运动,线段
的中点的轨迹方程为E.
(1)求轨迹方程
;
(2)过点
的直线
与曲线E交于P,Q两点,若
,其中O为坐标原点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/356547c08d2cd7ba5a6aaf412266d7b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c25b4d3207ab7c0bc74255ebb9a86f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(1)求轨迹方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](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/5913bd66d21e7f78c7573dfef4945194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2021-11-19更新
|
662次组卷
|
3卷引用:第2章 直线和圆的方程(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
(已下线)第2章 直线和圆的方程(基础、典型、新文化、压轴)分类专项训练-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)广东省湛江市第二十一中学2021-2022学年高二上学期期中数学试题(已下线)高二上学期期中【压轴60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)
2021高二·江苏·专题练习
解题方法
10 . 已知平面直角坐标系中有两定点
,
,平面中有一动点M,该点使得
满足条件
,则
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f7a7cf83fb9706134edb619d8aa90a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6cc3f576dcf32e3ec2de59ea8059a4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bd4a70ff777ba348ead2984d24bd362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f4dae5397232f44d0051fae1b0bd39.png)
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