2023高二上·全国·专题练习
1 . 已知两条直线
,
,若
与
相交,则实数a满足的条件是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6aa5c716e64aac90abdd313e8a6be85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebd12fd72dd59e5e2e7db019092a2d4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2 . (1)若直线
的斜率存在,则直线
的斜率
与倾斜角
的关系为______________ .
(2)斜率存在的两条的直线
,
(其中
),若
,则_____________ ;若
,则__________ .
(3)
,
,则
两点的中点坐标为_________________ .
(4)已知点
,直线
(其中
不全为0),那么点
到直线
的距离公式为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
__________ .(其中
不全为0)
(5)圆的半径
,圆心到直线的距离
,若圆与直线相切,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
____
;若直线与圆相交,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
____
;直线与圆相交的弦长![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(2)斜率存在的两条的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa4211831377655be51acaf182280085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266e3689cc366d5f0a7718ce9c20e818.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222f64d83170dc4dbab1e9cfb6924720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1095c036b49c3327baaa2c3c7f746134.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(4)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2206f341b1ae7d0f7f6d838b09c0b21.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c98c59cd4749afdd21e73529fc84323.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(5)圆的半径
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/050294162a78c6f4d6a87849bd3049a3.png)
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3 . 若直线
的方程为
,
的方程为
,则直线
与
的关系是_______ .(填“平行”或“垂直”);
与
的距离是___________ ..
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74005713904f58e71ecbf079a19d2085.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b740d1f7ec8da97b4bd1f55378f9fbe.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)
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22-23高二·全国·课后作业
4 . 两条直线都有斜率而且不重合时,如果它们平行,那么它们的____ 相等;反之,如果它们的斜率相等,那么它们____ ,即
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7c6adf233b234628fd9a25539a00b3b.png)
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2022高二上·全国·专题练习
5 . 若
与
为两条不重合的直线,它们的倾斜角分别为
,
,斜率分别为
,
,则下列命题
①若
,则斜率
; ②若斜率
,则
;
③若
,则倾斜角
;④若倾斜角
,则
;
其中正确命题的个数是______ .
![](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/e72adb45c60c2f63b46e65ff787302bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e88093a749c0d46e0ee931ecfaff925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53ea3373af8c2c835a1bfbe2c742d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c53ea3373af8c2c835a1bfbe2c742d8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
③若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b2fb1017d5dfe3a300de3e14a71b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b2fb1017d5dfe3a300de3e14a71b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cdb9d8425d73a68731f30e0c0e22260.png)
其中正确命题的个数是
您最近一年使用:0次
2022-07-17更新
|
1340次组卷
|
8卷引用:2.2 直线的位置关系
(已下线)2.2 直线的位置关系(已下线)专题34 两条直线的位置关系-4广西玉林市博白县第四中学(博白县中学书香校区)2022-2023学年上学期高二9月月考数学试题2.3.1 两直线的平行与垂直(同步练习提高版)(已下线)第02讲 2.1.2两条直线平行和垂直的判定(5 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)2.1.2 两条直线平行和垂直的判定【第一练】(已下线)1.3 两条直线的位置关系(十大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)(已下线)专题1.3 两条直线的平行与垂直(2个考点五大题型)-2023-2024学年高二数学《重难点题型·高分突破》(苏教版2019选择性必修第一册)
21-22高二·全国·课后作业
6 . 判断正误
(1)若两条不重合的直线的倾斜角相等,则这两条直线必定平行.( )
(2)若两条直线平行,则这两条直线的倾斜角一定相等.( )
(1)若两条不重合的直线的倾斜角相等,则这两条直线必定平行.
(2)若两条直线平行,则这两条直线的倾斜角一定相等.
您最近一年使用:0次
解题方法
7 . 有下列命题:
①若两条直线平行,则其斜率必相等;
②若两条直线的斜率乘积为
,则其必互相垂直;
③过点
,且斜率为
的直线方程是
;
④同垂直于
轴的两条直线一定都和
轴平行;
⑤若直线的倾斜角为
,则
.
其中为真命题的有________________ (填写序号).
①若两条直线平行,则其斜率必相等;
②若两条直线的斜率乘积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
③过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/508fa4303c29161b939ff98d6721be17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648411e9f7a212df0ccd7b7e06241bca.png)
④同垂直于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
⑤若直线的倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9c89eab34f319912ed5efb3f6f4592c.png)
其中为真命题的有
您最近一年使用:0次
2021高二·江苏·专题练习
8 . 已知直线
的倾斜角为
,直线
经过点
,
,则直线
与
的位置关系是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea191cdc92920c76fe66702d99130fd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/656737c0948940542ad9a89f88b13e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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9 . 两条直线的夹角的取值范围为______ .
您最近一年使用:0次
2021-01-18更新
|
93次组卷
|
3卷引用:上海市黄浦区2020-2021学年高二上学期期末数学试题
上海市黄浦区2020-2021学年高二上学期期末数学试题沪教版(2020) 选修第一册 精准辅导 第1章 1.3(3) 两直线夹角的求法(已下线)1.3两条直线的位置关系(作业)(夯实基础+能力提升)-【教材配套课件+作业】2022-2023学年高二数学精品教学课件(沪教版2020选修第一册)
10 . 直线
和直线
的位置关系是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6781ebb477443c6f7955284db11eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19556a290cd4e98e84b584d30f466614.png)
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2020-06-25更新
|
322次组卷
|
4卷引用:沪教版(上海) 高二第二学期 新高考辅导与训练 第11章 坐标平面上的直线 阶段训练2