名校
1 . 如图,在四棱锥
中,平面
平面
,点E在以
为直径的半圆O上运动(不包括端点),底面
为矩形,
.
平面
;
(2)当四棱锥
体积最大时,求平面
与平面
所成夹角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf9a6db3571fa57bfa2d5e4d44c51b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c09afc70f448545336304333d5b5658b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fceb227a6d222aa08c39f2e405aa119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662698361c6b3ddaf0c28a3c87be53e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
(2)当四棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80c753cb1eb73fd8d136d00462970797.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9a32bd7a1b78b5a0ec562c4025aea8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c66d99a6a8415ddad22bbed33b64cfb.png)
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名校
2 . 如图,在三棱柱
中,
,点
在底面ABC的射影为BC的中点,
为
的中点.
平面
.
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de3cc06de62b1310a38ef0cb6450b584.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56f7ba05c54b3de1f4378f7c8eb58328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4890e58791814622b87c4d60ea971f54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f10885aaa1e46c288f82c680857e1eeb.png)
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2024-05-08更新
|
647次组卷
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5卷引用:内蒙古自治区兴安盟2023-2024学年高二下学期学业水平质量检测数学试题
内蒙古自治区兴安盟2023-2024学年高二下学期学业水平质量检测数学试题河南省创新发展联盟2023-2024学年高二下学期4月期中数学试题贵州省遵义市2023-2024学年高二下学期5月期中联考数学试题(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)(已下线)专题02 空间向量与立体几何--高二期末考点大串讲(苏教版2019选择性必修第二册)
解题方法
3 . 已知双曲线
的虚轴长为
,点
在
上.设直线
与
交于A,B两点(异于点P),直线AP与BP的斜率之积为
.
(1)求
的方程;
(2)证明:直线
的斜率存在,且直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e90acecacaab778257a1a1e903b2028a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/4dac452fbb5ef6dd653e7fbbef639484.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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昨日更新
|
24次组卷
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2卷引用:内蒙古自治区锡林郭勒盟2024届高三下学期5月模拟考试理科数学试题
名校
4 . 如图,已知正三棱柱
分别为棱
的中点.
平面
;
(2)求二面角
的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08779b8f171e17017a891f876df7fc0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90fdf6f784f618a70fb4768f74aa970b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e16f65c3a318220c2f5baac171bbb61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41104641f3e2260d00aeadf8fb8a078a.png)
(2)求二面角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14588eb195962ce563e0c7a551510a48.png)
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2024-03-31更新
|
2839次组卷
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3卷引用:内蒙古赤峰市赤峰二中2023-2024学年高二下学期第一次月考数学试题
解题方法
5 . 已知椭圆
的右焦点为F,短轴长等于焦距,且经过点
.
(1)求椭圆E的方程;
(2)设过点F且不与坐标轴垂直的直线与E交于A,B两点,线段AB的中点为C,D是y轴上一点,且
,求证:线段CD的中点在x轴上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
(1)求椭圆E的方程;
(2)设过点F且不与坐标轴垂直的直线与E交于A,B两点,线段AB的中点为C,D是y轴上一点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b757f0c42ae5c9a2d6a4b19e5877b27.png)
您最近一年使用:0次
6 . 已知椭圆E:
的长轴为双曲线
的实轴,且离心率为
.
(1)求椭圆E的标准方程;
(2)已知椭圆
在其上一点
处的切线方程为
.过直线
上任意一点P作椭圆E的两条切线,切点分别为A,B.M为椭圆的左顶点.
①证明:直线
过定点;
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dad0c75ce33673ec4c425896e8619e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆E的标准方程;
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2c17005d48901a9f9d996e1c7c67eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46c2737bf9c790cdb4b767217719452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
①证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a5e0a51c9e14fb246b0ba0b231c1e3.png)
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7 . 如图,在平行六面体
中,E在线段
上,且
F,G分别为线段
,
的中点,且底面
为正方形.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/10/64aaaa44-e421-4524-b946-30f03c57691a.png?resizew=172)
(1)求证:平面
平面![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c480d2b007fa8675efc646f91e256df2.png)
(2)若
与底面
不垂直,直线
与平面
所成角为
且
求点 A 到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dcbb8f28f80f9908f58f2d152e912766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd774c50250550d1c90f37ced4c0e7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17eaf5287e999c0adfe22f544d8e0945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88929f4ba0851730d5f941d426b87548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/10/64aaaa44-e421-4524-b946-30f03c57691a.png?resizew=172)
(1)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7bde810ee34535aa397501889a52b44.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c480d2b007fa8675efc646f91e256df2.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0215e13a9fb5574d5194aeb9507a98aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8946331b0a9d86e1a9c78797f3021455.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3676ef5c9bde8f56ac5880b7f4aa1d6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fda6215d1e6cb84f6a360b684634ea7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/509356b0db34d34ff0fe25337a48e16a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d5e5c12362a66c14785327a528b6f4c.png)
您最近一年使用:0次
2024-03-06更新
|
1597次组卷
|
3卷引用:内蒙古自治区包头市2024届高三下学期适应性考试理科数学试题(二)
8 . 如图,在三棱锥
中,
的中点分别为
.
的长;
(2)证明:平面
平面
;
(3)求平面
和平面
夹角的余弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/607d2e6bf6337d559bcd3d45f1f45afb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/630201207817c1b492c50332eabebaa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)证明:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d7090639341730951c1bc3c9b6164e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7b7c83470489253394bd288d7c920df.png)
(3)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06bf006d9cf9568dd567c25fd20a0c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c0bfeadcf17b2a45896071f07a4a5a.png)
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2024-04-17更新
|
188次组卷
|
2卷引用:内蒙古自治区呼和浩特市第二中学2023-2024学年高二下学期4月月考数学试题
名校
解题方法
9 . 已知椭圆
的两个焦点分别为
,离心率为
.
(1)求椭圆
的标准方程;
(2)M为椭圆
的左顶点,直线
与椭圆
交于
两点,若
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/871868260c78a20767eae39bcdb97476.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)M为椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-10-03更新
|
3225次组卷
|
5卷引用:内蒙古自治区呼和浩特市第一中学2023-2024学年高二上学期期中数学试题
解题方法
10 . 已知椭圆
过点
,且焦距为
.
(1)求椭圆
的标准方程;
(2)过点
作两条互相垂直的弦
,设弦
的中点分别为
.证明:直线
必过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc3e47a358860345e74450ce2af9f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次