1 . 如图,在直三棱柱
中,
,
为棱
的中点,
,二面角
的大小为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/06a66602-3044-4524-9529-59d823918a91.png?resizew=209)
(1)求证:
平面
;
(2)求直线
与平面
所成角的正弦值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b6e4a2df58a236c20df5df0d29a466c.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/0685676650662a1f1a7dc762792979b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3e32f701757a5bf0c41cc3a7745fdd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/23/06a66602-3044-4524-9529-59d823918a91.png?resizew=209)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd597851c0db4e4de4769e10e09383b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0e7e39306c02ab9c0d606dbca6685e.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7f6f93171329d508d491143b9d71f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0e7e39306c02ab9c0d606dbca6685e.png)
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解题方法
2 . 下列结论中正确的是( )
A.若![]() ![]() ![]() |
B.若![]() ![]() ![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() ![]() |
D.若向量![]() ![]() ![]() ![]() ![]() |
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2023-12-23更新
|
428次组卷
|
3卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷
解题方法
3 . 已知圆
的圆心为
(
且
),
,圆
与
轴、
轴分别交于
,
两点(与坐标原点
不重合),且线段
为圆
的一条直径.
(1)求证:
的面积为定值;
(2)若直线
经过圆
的圆心,求圆
的方程;
(3)在(2)的条件下,设
是直线
上的一个动点,过点
作圆
的切线
,
,切点为
,
,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3b5fe7ff4823684bcbd303eb74833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045cf6c42c53f44921c55a01fc4cdd8c.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/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.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/803a617fb53e67edbc2955cb629c329b.png)
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4 . 已知空间中三点
,
,
.设
,
.
(1)求
;
(2)若
与
互相垂直,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/469780cd5a58a130d6edc45e0aee052b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbafeecf9ef82b8fa2802b8fe31b8d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82fb52b52abfc937fd9d0dd186ed83f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21841338587f28e2b8adbc39897a145b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04d418c27621284f0b1f68587178adc.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fb6118172f384a565afcdfd84e9cdb0.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5420712af80f88249f4a45cd0f3abbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8d5d06c8ba359e2f95bd6abbeb9d696.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-12-20更新
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327次组卷
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3卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷
解题方法
5 . 已知圆
经过
,
两点.
(1)求圆
的半径;
(2)判断圆
(
且
)与圆
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/693f2138ceb7dee28e012142fcbfccb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf8f5d8be251bf2848d6d10aa0340f9.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/458f692e00f30df65348237049473bf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6 . 已知圆
与圆
,则下列说法正确的是
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c1c01121e7c2a52ebe672eeecc38840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c691b4c8e9d3d50c179eb5850f930379.png)
![](https://img.xkw.com/dksih/QBM/2023/11/18/3370788760117248/3371178539253760/STEM/3f563d83b647455886b77838eb91139c.png?resizew=4)
A.圆![]() ![]() |
B.若圆![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
您最近一年使用:0次
2023-12-02更新
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3卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷
解题方法
7 . 经过点
,且以
为圆心的圆的一般方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e87b3d349194312a934fced615e563c.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次
2023-11-27更新
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530次组卷
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2卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷
解题方法
8 . 已知椭圆
的一个焦点和一个顶点在圆
上,则该椭圆的离心率不可能是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f34858a47da4ca7cc91dd40a91bb7ec.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
9 . 已知椭圆
的两个焦点为
,
,且焦距为4,点
在
上,若
的最大值为25,则
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e3df14e8b1b02dbda69bfbb06269cbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 已知A,B,C,D是空间中互不相同的四个点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f94481b5b90278632dabf31c07437f8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-11-23更新
|
369次组卷
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7卷引用:安徽省皖豫名校联盟2023-2024学年高二(上)期中考试数学试卷