名校
1 . 已知曲线
(
为常数).
(i)给出下列结论:
①曲线
为中心对称图形;
②曲线
为轴对称图形;
③当
时,若点
在曲线
上,则
或
.
其中,所有正确结论的序号是_________ .
(ii)当
时,若曲线
所围成的区域的面积小于
,则
的值可以是_________ .(写出一个即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa04668d4a84a4408755101ec5bcbf7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(i)给出下列结论:
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aed39f5aca78934fb383402433fe549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0636ea90e009f020392980f18bc648b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f575a1608f883f9a5a2354435726956.png)
其中,所有正确结论的序号是
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6c8951e515ff33eb8292e769d146885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-01-10更新
|
869次组卷
|
10卷引用:北京市海淀区2019-2020学年高三上学期期末数学试题
北京市海淀区2019-2020学年高三上学期期末数学试题(已下线)专题11 双曲线及其性质-2020年高考数学母题题源解密(北京专版)(已下线)专题09 曲线与方程——2020年高考数学母题题源解密(山东、海南专版)北京市第四十四中学2021届高三上学期期中考试数学试题江苏省南京师大附中2020-2021学年高二上学期12月阶段检测数学试题江苏省南通中学2020-2021学年高二上学期期末数学试题(已下线)卷20-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(北京专用)北京师范大学附属实验中学2022届高三12月统一练习数学试题北京师大实验中学2022届高三12月份月考数学试题(已下线)专题01 条件开放型【练】【北京版】
解题方法
2 . 古希腊数学家阿波罗尼奥斯的著作《圆锥曲线论》中记载有这样一个命题:平面内与两定点距离的比为常数
且
的点的轨迹是圆,后人将这个圆称为阿波罗尼奥斯圆.已知点
,圆
,在圆
上存在点
满足
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
__________ .(写出满足条件的一个
的值即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf56f44f995858afc4f6ae1306bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bb8775b827a649b07b6c2f8c3ea284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607f46a677204def6c4341ad0dc9922a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/585e81f117c173e2c021d9bacb985370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420d464c96149bd9cb5c7b1b3548133c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/258e40e3883271c3580c1d3c805dcac6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
您最近一年使用:0次
解题方法
3 . 已知椭圆
与直线l:
有唯一的公共点M.
(1)当
时,求点M的坐标;
(2)过点M且与l垂直的直线分别交x轴、y轴于
,
两点.当点M运动时,
(i)求点
的轨迹方程,并说明轨迹是什么曲线;
(ii)如果推广到一般椭圆,能得到什么相应的结论?(直接写出结论即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddab7b8aa22e1ba4c59da7dc04ac9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5464dc3bd349a216296fbaa879ae47.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
(2)过点M且与l垂直的直线分别交x轴、y轴于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93e5725eea66482aecf029044c404f24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d48001aa635215e2be1eed43a572621a.png)
(i)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
(ii)如果推广到一般椭圆,能得到什么相应的结论?(直接写出结论即可)
您最近一年使用:0次
4 . 如图,在棱长为
的正方体
中,
,
,
,
分别为棱
,
,
,
的中点,点
在四边形
及其内部运动,
是棱
上的点.当![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483c4accd0aeafc4a83ff960f4e5c4d.png)
__________ 时(在线上填入确定的常数),若
,则动点
的轨迹长为__________ (填写一组关系即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f66fb71b75b63594ebeeeebd1963eed5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d483c4accd0aeafc4a83ff960f4e5c4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f43488162b69d750f069b89a8b2d80f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/23/857f5a77-82d2-428a-b047-739420297b50.png?resizew=220)
您最近一年使用:0次
2022-03-31更新
|
428次组卷
|
3卷引用:湖北省黄石市有色一中2021-2022学年高二上学期10月月考数学试题
名校
5 . 对于曲线
有以下判断,其中正确的有__ (填上相应的序号即可).
(1)它表示圆;
(2)它关于原点对称;
(3)它关于直线
对称;
(4)
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f4f3d8ac7da6c1c186949ffc9c39a5.png)
(1)它表示圆;
(2)它关于原点对称;
(3)它关于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(4)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cdf5b2c1dbc688cb4e710ec58577ee5.png)
您最近一年使用:0次
名校
6 . 已知点
.若曲线
上存在两点
、
,使
为正三角形,则称
为
型曲线,给定下列四条曲线:
①
; ②
;
③
; ④
.
其中,属于
型曲线的是____________ (写出序号即可)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5a6145990adf5574f0e0f2fc828ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcd6ea45f6f945e5e614cad59949346.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a972c3642e125f123897984ca1c0361a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/991df64879833b7dbb0477fd75de7df5.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fa774e28b8077a6fef333e7dc83e68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15e413035bed8ce1485e790077e9d4d0.png)
其中,属于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efcd6ea45f6f945e5e614cad59949346.png)
您最近一年使用:0次
7 . 对于曲线
有以下判断:(1)它表示圆;(2)它关于原点对称;(3)它关于直线
对称;(4)
且
其中正确的有________ (填上相应的序号即可).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06f4f3d8ac7da6c1c186949ffc9c39a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a79d7f73b6128650bf7aed538260c72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eeafaa6479bcc807813868a124b56ff.png)
您最近一年使用:0次
8 . 圆
的半径为定长
是圆
上任意一点,
是圆
所在平面上与
不重合的一个定点,线段
的垂直平分线
和直线
相交于点
,当点
在圆上运动时,点
的轨迹可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9b59b77e7bd55e110e952b58923b8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
A.一个点 | B.椭圆 | C.抛物线 | D.双曲线 |
您最近一年使用:0次
9 . 已知定圆
,点
是圆
所在平面内一定点,点
是圆
上的动点,若线段
的中垂线交直线
于点
,则点
的轨迹可能是:①椭圆;②双曲线;③抛物线;④圆;⑤直线;⑥一个点.其中所有可能的结果有___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d815b1dd40ac542b3a9d10584da5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
名校
解题方法
10 . 阿波罗尼斯
古希腊数学家,约公元前
年
的著作
圆锥曲线论
是古代世界光辉的科学成果,它将圆锥曲线的性质网罗殆尽,几乎使后人没有插足的余地.他证明过这样一个命题:平面内与两定点距离的比为常数
且
的点的轨迹是圆,后人将这个圆称为阿波罗尼斯圆.现有圆C:
和点
,若圆C上存在点P,使
其中O为坐标原点
,则t的取值可以是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd995178601c2ad7b40f973d268c7bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a920f6a735734c54b41e188ceb969c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33b0e787c1d82071c825975348698f58.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/461950348087cdb06ec28d7569d14c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fbf56f44f995858afc4f6ae1306bdbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bb8775b827a649b07b6c2f8c3ea284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb077373c470866ffd54857fe7e747ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffc3d20dedf819e5fa002ffbd7b4e4ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2532a0069ba3716431e602b7441631c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
2022-04-13更新
|
1049次组卷
|
7卷引用:江苏省徐州市邳州市官湖中学2021-2022学年高二上学期第一次月考数学试题