名校
1 . 如图,已知定圆
,定直线
过
的一条动直线
与直线
相交于
,与圆
相交于
两点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3c884cb1-5f9f-403e-ae1e-c7f773ae969b.png?resizew=187)
(1)当
与
垂直时,求证:
过圆心
;
(2)当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
时,求直线
的方程;
(3)设![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
,试问
是否为定值,若为定值,请求出
的值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e85fc19d652ea7c8cd9236a17fc9c306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d2ecbf4eeb997be8293cadc7f71216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc304df70be14cccc9abea2c91e2fdb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dd8cb171425253834dfd7fa1a9da9ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/3c884cb1-5f9f-403e-ae1e-c7f773ae969b.png?resizew=187)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64c84a09595eabd6ae21a2e8faa7465c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/825116eb345f5505ebc8c1cdb8a1f131.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdc7bdc6448ef9a13c59fdce1b9bb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2020-01-06更新
|
764次组卷
|
5卷引用:2014-2015学年辽宁省朝阳区三校高二下学期第一次段测理科数学试卷
名校
2 . 在平面直角坐标系xOy中,圆O:
与坐标轴分别交于A1,A2,B1,B2(如图).
(1)点Q是圆O上除A1,A2外的任意点(如图1),直线A1Q,A2Q与直线
交于不同的两点M,N,求线段MN长的最小值;
(2)点P是圆O上除A1,A2,B1,B2外的任意点(如图2),直线B2P交x轴于点F,直线A1B2交A2P于点E.设A2P的斜率为k,EF的斜率为m,求证:2m﹣k为定值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/68b38476-f4c2-49d8-a645-6b93f7c230c6.png?resizew=428)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
(1)点Q是圆O上除A1,A2外的任意点(如图1),直线A1Q,A2Q与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b12dab697596b2417f0f2e945113bc40.png)
(2)点P是圆O上除A1,A2,B1,B2外的任意点(如图2),直线B2P交x轴于点F,直线A1B2交A2P于点E.设A2P的斜率为k,EF的斜率为m,求证:2m﹣k为定值.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/17/68b38476-f4c2-49d8-a645-6b93f7c230c6.png?resizew=428)
(图1) (图2)
您最近一年使用:0次
2018-12-11更新
|
463次组卷
|
5卷引用:辽宁省沈阳市第二十中学2021-2022学年高二上学期阶段验收数学试题
名校
3 . 在平面直角坐标系xOy中,已知圆C的方程为
,点
.
求过点M且与圆C相切的直线方程;
过点M任作一条直线与圆C交于A,B两点,圆C与x轴正半轴的交点为P,求证:直线PA与PB的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/259e9a874ba8a4fbc027e01699a81d8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50b70a5e6dd716c2d2fbeccfc255ee0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
您最近一年使用:0次
2018-08-15更新
|
2058次组卷
|
3卷引用:辽宁省名校联盟2022-2023学年高二上学期10月联考数学试题