23-24高二上·北京东城·期末
名校
1 . 在长方体
中,点
在矩形
内(包含边线)运动,在运动过程中,始终保持到顶点
的距离与到对角线
所在直线距离相等,则点
的轨迹是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab41cce6eb2d3058a644314865d16548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.线段 | B.圆的一部分 |
C.椭圆的一部分 | D.抛物线的一部分 |
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2 . 已知正方体
的棱长为
,
为
的中点,
为
所在平面上一动点,
为
所在平面上一动点,且
平面
,则下列命题正确的是______________
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/a5c36a18-e9d3-4f07-8c88-a3a8523a8c41.png?resizew=157)
①若
与平面
所成的角为
,则点
的轨迹为圆
②若三棱柱
的表面积为定值,则点
的轨迹为椭圆
③若点
到直线
与直线
的距离相等,则点
的轨迹为抛物线
④若
与
所成的角为
,则点
的轨迹为双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22adbc0da438220f9cace11b629d799b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7688363f5ffff23a6193c7a8eee501c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89ab6fd9972d6298ae91e81cb75189a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/25/a5c36a18-e9d3-4f07-8c88-a3a8523a8c41.png?resizew=157)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15615de1a6df206dbd081251f676578e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
②若三棱柱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3650dbd33494476747a678d4038bf7f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
③若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a851907ada2ac2c3c4880a6736d28a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e52a8f07834cbbbe4224962672fbbb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
④若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9932b14d1f7f381263281a50100c27b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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3 . 曲线
是平面直角坐标系内与两个定点
和
的距离之积等于4的点的轨迹,则( )
①曲线
过原点;
②曲线
关于原点对称;
③若点
在曲线
上,则
的面积不大于2;
④曲线
与曲线
有且仅有两个交点.
其中正确命题的序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
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若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
其中正确命题的序号为( )
A.①② | B.②③④ | C.③④ | D.①②④ |
您最近一年使用:0次
2023-11-13更新
|
324次组卷
|
2卷引用:北京市汇文中学2023-2024学年高二上学期期中考试数学试题
2023高二·上海·专题练习
名校
4 . 关于曲线
:
,则以下结论正确的序号是____
①曲线
关于原点对称;
②曲线
中x∈[﹣2,2],y∈[﹣2,2];
③曲线
不是封闭图形,且它与圆x2+y2=8无公共点;
④曲线
与曲线
:
有4个交点,这4点构成正方形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b853f6a19a68fe116a7d83533891f89.png)
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曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f141f1db0a086c059024615fb5ac18d.png)
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解题方法
5 . 如图,在四棱锥
中,底面
是边长为3的正方形,
平面
,点M为底面上的动点,M到
的距离记为d,若
,则点M在底面正方形内的轨迹的长度为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/e7522e7d-3b86-4d1a-8772-8ca5a66c2ee5.png?resizew=179)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41e2de7c6600c3dc4d6a37f382792077.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/6/e7522e7d-3b86-4d1a-8772-8ca5a66c2ee5.png?resizew=179)
A.2 | B.![]() | C.![]() | D.![]() |
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2023-01-05更新
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691次组卷
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4卷引用:北京市东城区2023届高三一模数学试题查漏补缺练习试题(2)
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6 . 已知曲线E的方程为
,给出下列四个结论:
①若点
是曲线E上的点,则
,
;
②曲线E关于x轴对称,且关于原点对称;
③曲线E与x轴,y轴共有4个交点;
④曲线E与直线
只有1个交点.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ffb138fc843a9ef427273804c759e5c.png)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f417f76e2e7eb5231d8e90fb85c5b17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95cccdff49c3efe6e7a7dbbf69db9319.png)
②曲线E关于x轴对称,且关于原点对称;
③曲线E与x轴,y轴共有4个交点;
④曲线E与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d585d2d6643471640905d234d9538c5.png)
其中所有正确结论的序号是
您最近一年使用:0次
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2卷引用:北京市东城区第一六六中学2023-2024学年高二上学期期末模拟数学试题
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解题方法
7 . 在平面直角坐标系
中,动点
到两坐标轴的距离之和等于它到定点
的距离,记点
的轨迹为
.给出下面四个结论:①曲线
关于原点对称;②曲线
关于直线
对称;③点
在曲线
上;④在第一象限内,曲线
与
轴的非负半轴、
轴的非负半轴围成的封闭图形的面积小于
.其中所有正确结论的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b47489a68843a5ee6f542c442b0ea547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/f89eef3148f2d4d09379767b4af69132.png)
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7卷引用:北京市东城区第一七一中学2024届高三上学期12月月考数学试题
北京市东城区第一七一中学2024届高三上学期12月月考数学试题(已下线)2023高考考前突破选填专题(北京)人教B版(2019) 选修第一册 北京名校同步练习册 第二章 平面解析几何初步 本章测试2020届北京市育英中学高三3月月考数学试题北京首师附中2021~2022学年高二上学期1月月考数学试题(已下线)北京市第四中学2022届高三下学期阶段性测试一数学试题北京市第一六一中学2023-2024学年高二下学期开学测试数学试题