1 . 由伦敦著名建筑事务所SteynStudio设计的南非双曲线大教堂惊艳世界,该建筑是数学与建筑完美结合造就的艺术品.若将如图所示的大教堂外形弧线的一段近似看成双曲线
(
,
)下支的部分,且此双曲线两条渐近线方向向下的夹角为
,则该双曲线的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/9fc7d104-4c5c-46aa-9224-08d2ccc9ed62.png?resizew=128)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/972012c1-7303-4e49-8967-4ed0a6d6570f.png?resizew=136)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b26461529321c5e669bdf3c489c5d74.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/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/9fc7d104-4c5c-46aa-9224-08d2ccc9ed62.png?resizew=128)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/17/972012c1-7303-4e49-8967-4ed0a6d6570f.png?resizew=136)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-17更新
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1355次组卷
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3卷引用:广东省梅州市2023届高三一模数学试题
2 . 已知三棱柱
中,
,
,且
,
,侧面
底面
,
是
的中点.
平面
;
(2)在棱
上是否存在点
,使得
与平面
的所成角为60°.如果存在,请求出
;如果不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fffa3d9c32da53b0ea0c338012ea20c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d960679bc2aa81f9100bcced84dbc20e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f2e238b2757353026133bbe495645e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eff0db05826cbff651faf0144904b32.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.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/d24243a33f3ad70cec7d4e15297d11e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efb87785b2842459c59b2571aac7374b.png)
(2)在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2777840758e70e7dbbc18cef8f3d6d2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a934b31dd77112ee7be67ecaf46fcad6.png)
您最近一年使用:0次
解题方法
3 . 已知双曲线
的左、右焦点分别为
、
,
且双曲线
经过点
.
(1)求双曲线
的方程;
(2)过点
作动直线
,与双曲线的左、右支分别交于点
、
,在线段
上取异于点
、
的点
,满足
,求证:点
恒在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96c4088276acdbede4781b2ebc466366.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/9efbe4a54a27dc48e3f52d6249bd1681.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f61a4f49d47ad1c1109275370214963.png)
(1)求双曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad01b0639b0b618c9128df2a5d1315c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
您最近一年使用:0次
2023-04-13更新
|
1277次组卷
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4卷引用:广东省梅州市2023届高三二模数学试题
名校
解题方法
4 . 如图所示,四边形ABCD为圆柱ST的轴截面,点Р为圆弧BC上一点(点P异于B,C).
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
,
(
),且二面角
的余弦值为
,求
的值.
![](https://img.xkw.com/dksih/QBM/2024/1/12/3409766460112896/3409781363875840/STEM/33b6f8354020463fba0be06f8057252b.png?resizew=147)
(1)证明:平面PAB⊥平面PAC;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8798f21caf1819d47db778d23fa57b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f2590902f4edd2fa6b233ef54a31862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/540ccd15435aa2d59e809d6a28fb2467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d80c787eefc6da2a49d25d2caeaa5fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e64e76a4c1e5934f51cdca2ffbc8313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2024-01-12更新
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1137次组卷
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5卷引用:广东省梅州市梅县东山中学2024届高三上学期期末数学试题
名校
5 . 如图,在四棱锥
中,底面
为直角梯形,
,
,
,
,
为
的中点,且
.记
的中点为
,若
在线段
上(异于
、
两点).
(1)若点
是
中点,证明:
面
;
(2)若直线
与平面
所成角的正弦值为
,求线段
的长.
![](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/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a0e5697eca3f5205cb7b343648240bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febdb95e8536e7000ad25c4ce1207665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eac224254ec674dddd13169a6381d974.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d4fb1fe5859dd21a6efd4feae51a17e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/8/a3c2977e-763d-4f69-9cae-0913bbed9f5f.png?resizew=189)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e582d73b96ba649378379c3074d506d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab52a9c7f7b361ad0488f01d714135fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
您最近一年使用:0次
2023-09-06更新
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1114次组卷
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6卷引用:广东省梅州市大埔县虎山中学2024届高三上学期第二次段考(10月)数学试题
名校
解题方法
6 . 如图,一个装有某种液体的圆柱形容器固定在墙面和地面的角落内,容器与地面所成的角为
,液面呈椭圆形状,则该椭圆的离心率为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac09dc1ca2cdd7aef28c218763d3e4d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/14/62ba3685-2622-4c32-9592-b8447633fa38.png?resizew=173)
您最近一年使用:0次
2023-04-13更新
|
1145次组卷
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6卷引用:广东省梅州市2023届高三二模数学试题
广东省梅州市2023届高三二模数学试题(已下线)专题06 解析几何专题19平面解析几何(填空题)(已下线)模块六 专题7易错题目重组卷(广东卷)江苏省镇江市句容碧桂园学校2022-2023学年高二下学期期中数学试题江苏省淮安市淮阴中学2023-2024学年高二上学期10月阶段练习数学试题
名校
解题方法
7 . 在长方体
中,
,
,动点
在体对角线
上(含端点),则下列结论正确的有( )
![](https://img.xkw.com/dksih/QBM/2022/4/13/2957152542466048/2957342903926784/STEM/8bf76c1fa43f4ca6a2a2e2c99750aa73.png?resizew=199)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/006c1fca04581d10987540a84fe22dfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4acc5d21a7490e6bed2453cc5147c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fe734023d4e70010a6b2cc3267cb86e.png)
![](https://img.xkw.com/dksih/QBM/2022/4/13/2957152542466048/2957342903926784/STEM/8bf76c1fa43f4ca6a2a2e2c99750aa73.png?resizew=199)
A.当![]() ![]() ![]() |
B.存在点![]() ![]() ![]() |
C.![]() ![]() |
D.顶点![]() ![]() ![]() |
您最近一年使用:0次
2022-04-13更新
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2346次组卷
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12卷引用:广东省梅州市2022届高三二模数学试题
广东省梅州市2022届高三二模数学试题(已下线)押新高考第12题 立体几何-备战2022年高考数学临考题号押题(新高考专用)(已下线)专题41:空间距离向量求法-2023届高考数学一轮复习精讲精练(新高考专用)江苏省镇江第一中学2021-2022学年高二下学期期中数学试题江苏省南京市、镇江市部分名校2021-2022学年高二下学期期中数学试题江苏省泰州中学2021-2022学年高二下学期第二次质量检测数学试题湖南省邵阳市第二中学2021-2022学年高一下学期期末数学试题广东省佛山市顺德区德胜学校2022-2023学年高二上学期期中数学试题安徽省芜湖市普通高中2022-2023学年高二上学期期中联考数学试题江西省上高二中2022-2023学年高二上学期期中数学小练卷试题(1)广东省深圳市深圳实验学校高中园(明理、卓越、崇文、至臻联考)2023-2024学年高二上学期期中数学试题重庆市第七中学校2023-2024学年高二上学期第四次月考数学试题
名校
解题方法
8 . 关于正方体
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
A.直线![]() ![]() |
B.若平面![]() ![]() ![]() ![]() |
C.棱![]() ![]() ![]() |
D.若正方体棱长为2,P,Q分别为棱![]() ![]() |
您最近一年使用:0次
2022-06-05更新
|
2304次组卷
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7卷引用:广东省梅州市丰顺县丰顺中学2022-2023学年高三上学期期末考试数学试题
广东省梅州市丰顺县丰顺中学2022-2023学年高三上学期期末考试数学试题(已下线)2022年全国新高考Ⅰ卷数学试题变式题20-22题(已下线)2022年全国新高考Ⅰ卷数学试题变式题9-12题2023年新高考全国I卷数学仿真模拟试卷(已下线)模块五 空间向量与立体几何-1江苏省镇江中学2021-2022学年高一下学期5月月考数学试题广东省珠海市斗门区第一中学2022-2023学年高二上学期期中数学试题
名校
解题方法
9 . 已知双曲线
的焦距为
,点
在
上.
(1)求
的方程;
(2)直线
与
的右支交于
,
两点,点
与点
关于
轴对称,点
在
轴上的投影为点
.
(ⅰ)求
的取值范围;
(ⅱ)求证:直线
过点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83bf4fd84818abac17a9d21237ac5ce5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd0c551cfc411bdb73d2d94e72a274ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f51698f7095e795d4f0527b986ac1db2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(ⅰ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a771f2e80c8a29ed2ebd76498b0f49.png)
(ⅱ)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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2024-05-13更新
|
1210次组卷
|
3卷引用:广东省梅县东山中学2024届高三下学期第一次模拟考试数学试题
名校
10 . 常言道:“不经历风雨,怎么见彩虹”.就此话而言,“经历风雨”是“见彩虹”的( )
A.充分不必要条件 | B.必要不充分条件 |
C.充要条件 | D.既不充分也不必要条件 |
您最近一年使用:0次
2024-04-17更新
|
1044次组卷
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2卷引用:广东省梅州市2024届高三下学期总复习质检(二模)数学试题