名校
解题方法
1 . 如图,设正方体
的棱长为
,点
是
的中点,点
为空间内两点,且
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23d7ef454aa07765aeea22895988b2fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0130321c5392fba6973f9e78e5b531c7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/4/39469988-c744-442e-9211-6b5157956797.png?resizew=160)
A.若![]() ![]() ![]() ![]() |
B.设![]() ![]() ![]() |
C.平面![]() ![]() ![]() |
D.若![]() ![]() ![]() |
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2024-01-03更新
|
1469次组卷
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4卷引用:河南省TOP二十名校2024届高三上学期调研考试九数学试卷
河南省TOP二十名校2024届高三上学期调研考试九数学试卷广东省广州市广东实验中学2024届高三上学期大湾区数学冲刺卷(四)广东省汕头市金山中学2024届高三上学期第一次模拟考试数学试题(已下线)模块7 空间几何篇 第2讲:立体几何的截面问题【练】
2 . 在极坐标系Ox中,圆
,直线
.
(1)在以O为原点,极轴为x轴的正半轴建立的直角坐标系xOy中,求C的标准方程和l的方程;
(2)以M为圆心的圆与圆C外切,且与l也相切,求M轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6add881073ca71a7a55af4c2f25317f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95fc45ef428d2de0bf23b66d0e7dc2f4.png)
(1)在以O为原点,极轴为x轴的正半轴建立的直角坐标系xOy中,求C的标准方程和l的方程;
(2)以M为圆心的圆与圆C外切,且与l也相切,求M轨迹的极坐标方程.
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2023-10-12更新
|
320次组卷
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4卷引用:河南省名校教研联盟2023届高三下学期5月押题考试理科数学试题
河南省名校教研联盟2023届高三下学期5月押题考试理科数学试题河南省名校教研联盟2023届高三下学期5月押题考试文科数学试题(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(九)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(九)
3 . 圆
,圆心为
,点
,作圆上任意一点
与
点连线的中垂线,交
于
.
(1)求
的轨迹
的方程;
(2)设
为曲线
上任意一点,直线
分别交曲线
于
两点,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71e8ffd8a6f46d6076861da6157e8274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513eafd10fa1ec0196562865517e0b09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebbacdeeb19a70460202e651fb6d77f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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4 . 在平面直角坐标系
中,曲线
的参数方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac9b5af135ada982f4b3013c6f8d1b0.png)
为
上的动点,点
满足
,设点
的轨迹为曲线
,以
为极点,
轴正半轴为极轴建立极坐标系.
(1)写出曲线
的极坐标方程;
(2)直线
(
,
),与曲线
交于点
(不同于原点),与曲线
:
交于点
(不同于原点),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac9b5af135ada982f4b3013c6f8d1b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/096d76252cd0a243d990354e679a4510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17f5d2e8186f0173d7862b1d39fb3dc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fece79e7cf22f4a2b0a27c4347e2546.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76c516619a5b3c6676e6734efa754e5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9281fe131dbc46c78527a4779ee9700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2023-08-05更新
|
499次组卷
|
4卷引用:河南省TOP二十名校2023届高三下学期3月调研模拟文科数学试题
解题方法
5 . 正方体
的棱长为
,
为
中点,
为平面
内一动点,若平面
与平面
和平面
所成锐二面角相等,则点
到
的最短距离是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11ddc92d84d188c66b435664a7e7b5a4.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/29a30fda2c8d6c44eac2a63ccad0da01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab3e0dba5705e1d749cfb21ebbb2ed93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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名校
解题方法
6 . 在平面直角坐标系
中,点
到两个定点
,
的距离的积等于
,记点
的轨迹为曲线
,则下列说法不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.曲线![]() | B.![]() ![]() |
C.![]() ![]() | D.点![]() ![]() |
您最近一年使用:0次
7 . 在长方体
中,
,
,点P在底面ABCD的边界及其内部运动,且满足
,则下列结论不正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5441d73845911db1993bf903c4d8700f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8d927585a17c2e98ef7d5a9589a26ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4b3cb4c667b4e6d0e14922e552ac95b.png)
A.若点M满足![]() ![]() |
B.点P到平面![]() ![]() |
C.若点M满足![]() ![]() |
D.当BP=3时,四面体![]() ![]() |
您最近一年使用:0次
2023-06-22更新
|
1492次组卷
|
3卷引用:河南省郑州市等3地2022-2023学年高三下学期6月冲刺卷(五)全国卷理科数学试题
河南省郑州市等3地2022-2023学年高三下学期6月冲刺卷(五)全国卷理科数学试题河南省郑州市等3地2022-2023学年高三下学期6月冲刺卷(五)全国卷文科数学试题(已下线)第一章 空间向量与立体几何(压轴题专练,精选20题)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)
解题方法
8 . 已知正方体
的棱长为
,动点P在
内,满足
,则点P的轨迹长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c510b85dfbca0e3ab0744655d77e8c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df0c421fdccdc5fa752dc2416b9897d.png)
您最近一年使用:0次
名校
9 . 如图,在棱长为1的正方体
中,
是截面
上的一个动点(不包含边界),若
,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31e53b212640dadf751ef7f65a78a209.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3bf2214aa6ae92d8da5511f946ba0069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/25/a37c12d0-0ff2-47c8-8b82-9ff15e4e8309.png?resizew=155)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-05-09更新
|
1023次组卷
|
5卷引用:河南省豫南名校毕业班2023届高三仿真测试三模文科数学试题
10 . 已知抛物线
的焦点
到准线的距离为2,直线
与抛物线
交于
两点,过点
作抛物线
的切线
,若
交于点
,则点
的轨迹方程为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82ea1be9b9b6bb12afa7e1ce703d1603.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bb345989b8e6b19edb6983e58705eaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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