1 . 如图,正方形ABCD和平面四边形ACEF所在的平面互相垂直,
平面
,
⊥
,
,
.
平面
.
(2)求证:平面
平面
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06222ee533c2484ab25321a6abbf98cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a477603f3f88c3b48352b6130f9ad5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ea52361458ce2e49ed0fe99d8e6c02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560439a9b6c535ff5037c950283371cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/932a04304f2d4975955d4baabb2deeea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ae8768996ca9a0f2c5d9a19abbd54df.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8f5ba965420dfd5aa4da211682df096.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134ef0b1a2669a09f05bd4dc2496f706.png)
您最近一年使用:0次
名校
解题方法
2 . (1)已知一条动直线
,求证:直线恒过定点,并求出点
到动直线的最大距离.
(2)若直线
与
轴的正半轴分别交于
两点,
为坐标原点,是否存在直线同时满足下列条件;①
的周长为12;②
的面积为6,若存在,求出方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8f74be3ca5c56fd3de40e92d0b303db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b3015886625ea8c2560142473ef65bf.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
您最近一年使用:0次
名校
解题方法
3 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
分别为棱
中点.
平面
;
(2)若平面
⊥平面
,求证:
;
(3)若平面
⊥平面
,且
,求直线
与平面
所成角.
![](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/003ed9a31cd7c06dbf6eba32471d60c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/369b118472338c30204f8118f4db936c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e5680d463aa0e74316ec3db2359397.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f20ac8cec1d644e24eb900915d8b724.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b31fb036fa1bb4aa5edfd369f49b45b.png)
(2)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bafa8c14100a4f847b41b9148954116c.png)
(3)若平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90301c045e3b639487f30fa24fd05a96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627a50d77ab7386c33f49f1845c98c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
您最近一年使用:0次
2023-11-14更新
|
767次组卷
|
3卷引用:江苏省无锡市辅仁高级中学2023-2024学年高一下学期5月月考数学试卷
江苏省无锡市辅仁高级中学2023-2024学年高一下学期5月月考数学试卷上海市川沙中学2023-2024学年高二上学期期中数学试题(已下线)第10讲 空间的垂直关系-【寒假预科讲义】(人教A版2019必修第二册)
名校
解题方法
4 . 如图,正方形ABCD中,点E,F分别为AB,BC的中点.将
,
,
分别沿DE,EF,DF折起,使A,B,C三点重合于点P.
(1)求证:
平面PEF;
(2)若
,且K为PD的中点,求三棱锥
的体积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c771a4feb150ad9cff8d70431c97eb17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2ea13010e2399194be2a681310543e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13668f033d00acfc366f7e47949c4462.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/8/3/a7b4ec8d-82f9-4da6-8ceb-a7994605f8b2.png?resizew=289)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a1b49f64e0065edad868b25e9fcada3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bda07c14d4081eaf41d036b26503d54.png)
您最近一年使用:0次
2023-08-02更新
|
589次组卷
|
2卷引用:江苏省常州市华罗庚中学2023-2024学年高三夏令营学习能力测试数学试题
名校
解题方法
5 . 如图,平面直角坐标系内,
为坐标原点,点
在轴正半轴上,点B在第一象限内,.
![](https://img.xkw.com/dksih/QBM/2023/10/14/3345721260736512/3346010836754432/STEM/5b12ab3a73af47b8ad452c6515bd3746.png?resizew=174)
(1)若
,求
的面积的最大值和取得
面积最大值时的直线
的方程;
(2)设
,若
,求证:直线
过一定点,并求出此定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://img.xkw.com/dksih/QBM/2023/10/14/3345721260736512/3346010836754432/STEM/5b12ab3a73af47b8ad452c6515bd3746.png?resizew=174)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/368fc197b61e01fe6a4a168bb7b375cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07238c84ee055801424700b0939224ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b82e0326fbbdacb67f2ed8cbbd0e5ef4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
6 . 已知圆
,直线
.
(1)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:过点
的圆过定点,并求出所有定点的坐标;
(2)若点P在直线l上运动,过点P作圆O的两条切线
,切点分别为
,求证:直线AB过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1bba341d6dc102851c557072f738ff3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82503069ae1dda33bb96fdddbe1c87c6.png)
(1)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97e7f54c3c611633cf0e2fe218d89460.png)
(2)若点P在直线l上运动,过点P作圆O的两条切线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
您最近一年使用:0次
名校
解题方法
7 . 如图,在四棱锥
中,底面
是平行四边形,
交
于点
,
是
上一点且
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
为
的中点;
(2)在线段
上是否存在点
,使得平面
平面
,若存在,请给出点
的位置,并证明,若不存在,请说明理由.
![](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/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa69a2247ad4d5231aa361349b12f97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
(2)在线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392e71a9d1ebe4577f785581d0142305.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
您最近一年使用:0次
2023-07-04更新
|
741次组卷
|
7卷引用:江苏省南京师范大学附属中学2022-2023学年高一下学期5月月考数学试题
江苏省南京师范大学附属中学2022-2023学年高一下学期5月月考数学试题(已下线)13.2.4 平面与平面的位置关系(1)-【帮课堂】(苏教版2019必修第二册)四川省内江市威远中学2023-2024学年高二上学期第一次月考数学试题(已下线)第10讲 8.5.3 平面与平面平行-【帮课堂】(人教A版2019必修第二册)(已下线)专题13.5空间平面与平面的位置关系-重难点突破及混淆易错规避(苏教版2019必修第二册)(已下线)专题3.5空间直线、平面的平行-重难点突破及混淆易错规避(人教A版2019必修第二册)(已下线)8.5.3 平面与平面平行-同步精品课堂(人教A版2019必修第二册)
8 . 如图,在直三棱柱
中,
,
,点
为
中点,连接
、
交于点
,点
为
中点.
(1)求证:
//平面
;
(2)求证:平面
平面
;
(3)求点
到面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78f7050f3151f3107611ddfef1709eef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/269c684310d0f7b5b9bf0a291e7ee748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ee8456443402a25b1e25d35ff7e1c98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24bb49fdc6b6bbb2449fdf8a0de769d3.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/f2eb89294b31ffdd2680b4361e8994d7.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/16/a478ba64-960a-42fc-a082-54cff1071d7b.png?resizew=141)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54415b35519030aaa5f7edf879f1160c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
您最近一年使用:0次
名校
解题方法
9 . 如图四边形ABCD是矩形,
平面BCE,
,点F为线段BE的中点.
平面ABE;
(2)求证:
平面ACF.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f9157fce2a8339d281178c7c0bccbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4fb90434b6da93bdc6590f769ef118b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44b190c8d3d7d7d0e6e959e8a52eae90.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b78172568aac9805d2ea2d5f742bf80c.png)
您最近一年使用:0次
2023-06-11更新
|
1892次组卷
|
5卷引用:江苏省徐州市沛县2022-2023学年高一下学期第二次学情调研数学试题
江苏省徐州市沛县2022-2023学年高一下学期第二次学情调研数学试题四川省成都市实验外国语学校2022-2023学年高一下学期期末数学试题湖南师范大学附属中学2022-2023学年高一下学期第二次大练习数学试题(已下线)第03讲 空间中平行、垂直问题10种常见考法归类(2)(已下线)专题训练:线线、线面、面面平行与垂直证明大题-同步题型分类归纳讲与练(人教A版2019必修第二册)
解题方法
10 . 设
为实数,直线
与直线
相交于点
.记
的轨迹为曲线
.
(1)求证:
;
(2)求曲线
的方程;
(3)是否存在斜率为
的直线
,使以
被曲线
截得的弦
为直径的圆过原点?若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98614da04fc086533fcb5457bf7ee73f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84f5d623a205b1cddb80f1e122954b6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce08b357f11ef44c3e8207ac574422a.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)是否存在斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-10-12更新
|
789次组卷
|
3卷引用:江苏省徐州市邳州市2023-2024学年高二上学期10月阶段性质量检测数学试题
江苏省徐州市邳州市2023-2024学年高二上学期10月阶段性质量检测数学试题内蒙古乌兰察布市四子王旗宽高实验学校2023-2024学年高二上学期期中数学试题(已下线)专题17 直线与圆的位置关系9种常见考法归类- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)