过点
的直线l分别交
与
于
两点.
(1)设
的面积为
,求直线l的方程;
(2)当
最小时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32dbb2986cbf7043fadb0933d24c6e8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/add2e829a19ff9c5598b1053c5d19923.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b3ffa6d247d9e0f00fcac11e023e3ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a316c27ccf35e5e9b4294364985927dc.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/559d66fd8b309fd440ce9bda78a579c9.png)
17-18高二上·上海徐汇·期中 查看更多[5]
上海市上海中学2017-2018学年高二上学期期中数学试题上海市建平中学2018-2019学年高二上学期12月月考数学试题(已下线)专题4.1 坐标平面上的直线【压轴题型专项训练】-2020-2021学年高二数学下学期期末专项复习(沪教版)(已下线)2.2 直线的方程-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)(已下线)专题04 直线的方程压轴题(4类题型+过关检测)-【常考压轴题】2023-2024学年高二数学上学期压轴题攻略(人教A版2019选择性必修第一册)
更新时间:2019-11-07 23:28:17
|
【知识点】 直线综合
相似题推荐
【推荐1】如图,
的直角边OA在x轴上,顶点B的坐标为
,直线CD交AB于点
,交x轴于点
.
![](https://img.xkw.com/dksih/QBM/2020/2/20/2402983145603072/2403669436899328/STEM/661b0f4e258548479a08355865c17a05.png?resizew=134)
(1)求直线CD的方程;
(2)动点P在x轴上从点
出发,以每秒1个单位的速度向x轴正方向运动,过点P作直线l垂直于x轴,设运动时间为t.
①点P在运动过程中,是否存在某个位置,使得
?若存在,请求出点P的坐标;若不存在,请说明理由;
②请探索当t为何值时,在直线l上存在点M,在直线CD上存在点Q,使得以OB为一边,O,B,M,Q为顶点的四边形为菱形,并求出此时t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6fbe3bcf4c7979b9d346e683c2844f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f218ffffbe34629983f0c71c9ca53b72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d01a94e44f605a4ad5315df763b3a352.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3606c0c68bc663f0d0785a2ba46ea4.png)
![](https://img.xkw.com/dksih/QBM/2020/2/20/2402983145603072/2403669436899328/STEM/661b0f4e258548479a08355865c17a05.png?resizew=134)
(1)求直线CD的方程;
(2)动点P在x轴上从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4fce41daba0da15b6b7fa1292a38789.png)
①点P在运动过程中,是否存在某个位置,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1585ebe7e539d6de4204d99c30fe1ca8.png)
②请探索当t为何值时,在直线l上存在点M,在直线CD上存在点Q,使得以OB为一边,O,B,M,Q为顶点的四边形为菱形,并求出此时t的值.
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解题方法
【推荐2】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”,如直线
:
,
:
是一组“
共轭线对”,其中O是坐标原点.
(1)已知
,
是一组“
共轭线对”,求
,
的夹角的最小值;
(2)已知点
、点
和点
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/a9faeed172ec5b88966b0d1c52748d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9faeed172ec5b88966b0d1c52748d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93a7f0bee85495117fd91d534cb0dd87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cadb861a4a12b5f7046e96f3cdca11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23bc3ddcefcd7b73135aeb5635f5c8f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26b0497e3acdf809152a83665cfe96e1.png)
(1)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74989eae06757ec5e0ffdd4272c23369.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d6e49afd31cfbaef00aa038020fabf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6de97dd16796c379c1e9691e40e788a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5880cfeb2885a0db3785917da2ba79f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/910ec9341909c0edd74ee755543c4c35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f82cfd620516c5812e213ed4e0534a1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c834005595ea1120e35c55d8f4dff9f.png)
(3)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384f2b0dd380c5d58495ffd20166869f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549e1d6be47f85dff5798858a53a9202.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9d9ccc4246c82939d8a659db9f28a87.png)
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(0.4)
真题
【推荐3】已知复数
和
,其中
均为实数,i为虚数单位,且对于任意复数z,有
.
(1)试求m的值,并分别写出
和
用x、y表示的关系式;
(2)将
作为点P的坐标,
作为点Q的坐标,上述关系可以看作是坐标平面上点的一个变换:它将平面上的点P变到这一平面上的点Q,当点P在直线
上移动时,试求点P经该变换后得到的点Q的轨迹方程;
(3)是否存在这样的直线:它上面的任一点经上述变换后得到的点仍在该直线上?若存在,试求出所有这些直线;若不存在,则说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa94ca0f83a56c76b274d2290069b7b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfb0097d548d31647157f08c1f9bc947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e76833a339bbdcb7ee1e8c1288da68b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29578ec97300cdfcbefcf7bcf757c6ce.png)
(1)试求m的值,并分别写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33101c0ba719d80774cbcd6893bce713.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b4d2174f411d9db6ab7b2aea47818cb.png)
(2)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a163c87c6eef71953b1b4d9e06d3d260.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
(3)是否存在这样的直线:它上面的任一点经上述变换后得到的点仍在该直线上?若存在,试求出所有这些直线;若不存在,则说明理由.
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