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1 . 已知
的三个顶点的坐标分别是点
与
,直线
.
(1)求边AC所在直线
的倾斜角和边AC上的高所在直线
的方程;
(2)记
为点
到直线
的距离,试问:
是否存在最大值?若存在,求出
的最大值:若不存在,说明理由;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/778e22498bd73dfa86d91d3560af6613.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/027edec53efa9c6a414fe55e6f8ae026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb697c1e490e549ef3ed64773e8b6937.png)
(1)求边AC所在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
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解题方法
2 . 已知倾斜角为
(
)的直线l与抛物线C:
(
)只有1个公共点A,C的焦点为F,直线AF的倾斜角为
.
(1)求证:
;
(2)若
,直线l与直线
交于点P,直线AF与C的另一个交点为B,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d34dc9cc44a91037bbc8d51fa4eb6a49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5858ee1ce52b251816757257a11c29.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dfab465486d4a4d33480f6a11ebf7ce.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/194b8ab194c7d299d5c3e0f09ec18384.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c98a7f3a8bf384b1dfc1d34aebd46d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0184d0b86796b9d2dd4d19a10293c7f7.png)
您最近一年使用:0次
2024-04-13更新
|
711次组卷
|
4卷引用:老华大联盟2024届高三下学期3月联考文科数学试卷(全国乙卷)
3 . 已知直线
过点
,
.
(1)若直线
的倾斜角为
,求实数
的值;
(2)若直线
的倾斜角为钝角,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c50f7b470a14ef21102166b8374265e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e396c83557ec8b2b4b12d97d6738819.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2023-11-19更新
|
134次组卷
|
4卷引用:河南省南阳市唐河县鸿唐高级中学2023-2024学年高二上学期8月月考数学试题
河南省南阳市唐河县鸿唐高级中学2023-2024学年高二上学期8月月考数学试题上海市建平世纪中学2023-2024学年高二下学期阶段练习1(3月)数学试卷(已下线)专题01 平面直角坐标系中的直线--高二期末考点大串讲(沪教版2020选修)(已下线)专题01平面直角坐标系中的直线全章复习攻略--高二期末考点大串讲(沪教版2020选修)
名校
4 . 1949年公布的《国旗制法说明》中就五星的位置规定:大五角星有一个角尖正向上方,四颗小五角星均各有一个角尖正对大五角星的中心点.有人发现,第三颗小星的姿态与大星相近.为便于研究,如图,以大星的中心点为原点,建立直角坐标系,
分别是大星中心点与四颗小星中心点的连接线,
,求第三颗小星的一条边
所在直线的倾斜角?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efe6a4e4a39301cf9d213034ff52d3ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a12faff51aef7939d0986b114e36843.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/29/46c78020-8ed3-4706-b0f1-72398d8ad474.png?resizew=166)
您最近一年使用:0次
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5 . 已知坐标平面内三点
,
,
.
(1)求直线AC的倾斜角;
(2)若D为
的AB边上一动点,求直线CD的倾斜角的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a16a46f03535c5af872fa8fa9f21a431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18d3bfa155ad67018da4d65815c5e5b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9946c5404c864e31e146ded1e58e5bf4.png)
(1)求直线AC的倾斜角;
(2)若D为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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解题方法
6 . 已知直线l的方程为
.根据以下条件,求直线m的方程.
(1)若直线m过点
,且直线m与直线l的夹角为
,求直线m的方程;
(2)若直线m的倾斜角为
,将直线m绕其上一点P逆时针旋转α后得到直线n,直线n与y轴交于点
,将直线n绕点P逆时针旋转
后得到直线l,求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3aa3adcb154f6144903d456289ecb0f.png)
(1)若直线m过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f700dfadb2d40a13c4797c368acc72d.png)
(2)若直线m的倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9ac7f5c2a744c676e60413cca43236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1803dc3c76fd2b51696647aa18602412.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d5d1dac32b2b62e28fcc24e92d0d00.png)
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7 . 根据下列条件,求直线
的倾斜角;
(1)斜率为
;
(2)经过
两点;
(3)一个方向向量为
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47153fdd73c0661fa460130082e30929.png)
(2)经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9852c6379f94d3394936114d4d212caf.png)
(3)一个方向向量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5d902a4bbfdb5925ed4650049e3d94.png)
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解题方法
8 . 已知平面直角坐标系内三点
.
(1)求直线
的斜率和倾斜角;
(2)若
可以构成平行四边形,且点
在第一象限,求点
的坐标及CD所在直线方程;
(3)若
是线段
上一动点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dbc7b6e7a079db5fc1a72ff5e36be36.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82a10b4f0c9323d726804c89dd9548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d301c349066cc3b8f4d37a7e221edec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02fe1b6f20cd9115202e23090f1ea9da.png)
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解题方法
9 . 已知
,
,
.
(1)求点
的坐标,满足
,
;
(2)若点
在x轴上,且
,求直线
的倾斜角;
(3)一条光线从点
发出,射到x轴上一点
后被x轴反射,求反射光线所在的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a39230682513cbb47a18a4e93cec8e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443db6b71418d897fdd83279aa8d3ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e40da75c36e4f2f072e72218cc4130.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7555f635da615b09b7e2f08ddbeaf1db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d049080729a41953717bbb40d3b03a1f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/230d1287b78d832a96414803e6323c45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
(3)一条光线从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443db6b71418d897fdd83279aa8d3ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9e40da75c36e4f2f072e72218cc4130.png)
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解题方法
10 . 在
中,点
的坐标为
,点
的坐标为
边上的中线所在直线的方程为
,直线
的倾斜角为
.
(1)求点
的坐标;
(2)过点
的直线
与
轴的正半轴、
轴的正半轴分别交于
两点,求
(
为坐标原点)面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630324de802b3b0911db1476e2194a2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86828a35c3cc5186e8029be94150edfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc568fbc1480ba87cfdc2b6b3c71200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/534de19db99087b564cd3e9ac4c4568c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f02028a3847c4807c2d3cf0ea7efb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2023-10-05更新
|
379次组卷
|
3卷引用:河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题
河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题河北省邢台市河北南宫中学2023-2024学年高二上学期第一次月考数学试题(已下线)期中考前必刷卷02(范围:第1章~3.2 提升卷)-2023-2024学年高二数学上学期期中考点大串讲(苏教版2019选择性必修第一册)