1 . 如图所示,椭圆
的上顶点和右顶点分别是
和
,离心率
,
,
是椭圆上的两个动点,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/f04e20f3-baf7-43bd-87e1-d2c1808ea034.png?resizew=203)
(1)求椭圆的标准方程;
(2)求四边形
面积的最大值;
(3)试判断直线
与
的斜率之积是否为定值,若是,求出定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98c8e36238ad90378e724466fcb6023.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/28/f04e20f3-baf7-43bd-87e1-d2c1808ea034.png?resizew=203)
(1)求椭圆的标准方程;
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(3)试判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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2 . 如图,已知四棱锥
的底面
是菱形,
,
为边
的中点,
,
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/29cad0d2-0e71-4784-b1bb-545ca841c52a.png?resizew=184)
(1)证明:
;
(2)试判断线段
上是否存在点
使得二面角
的余弦值为
,若存在求出点
的位置;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/f945a69cf7e8213e50622125cde652f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6428c8dffe141f24eb248f728099e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9791de7c9c09d3c8a0e3c74afa662898.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/29cad0d2-0e71-4784-b1bb-545ca841c52a.png?resizew=184)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9bb69be70ba0babb236757648695faca.png)
(2)试判断线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73dad31ce33dc5a58f015280ee7bf450.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/642a7dd471434c923f76809dfa5ee183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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6卷引用:湖北省武汉市新洲区部分学校2023-2024学年高二上学期期中质量检测数学试题
湖北省武汉市新洲区部分学校2023-2024学年高二上学期期中质量检测数学试题山东省新泰市第一中学东校2023-2024学年高二上学期第二次质量检测数学试题山东省新泰市第一中学东校2023-2024学年高二上学期第二次月考数学试题(已下线)模块一 专题1 立体几何(2)高三期末(已下线)模块五 专题4 期末全真模拟(能力卷2)期末终极研习室(高二人教A版)重庆市第一中学校2023-2024学年高二上学期期末模拟数学试题
名校
解题方法
3 . 如图,在四棱锥
中,已知:
平面
,
,
,
,已知
是四边形
内部一点(包括边界),且二面角
的平面角大小为
,若点
是
中点,则四棱锥
体积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce0d7095ddd69d6ceaf1065b1bc2c79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a755edadca4e4fc27fd49559b8d691ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1074c943acd591413af464a28c285f05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8787d38a2a6f1dbb0581ccff5ff24f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1a63ab608517bb10aa036783dfb51f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0779bf252723c0419ab5358cf1d5c0fe.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/30/b1148f7d-93b1-4bcb-a768-938026ee9a34.png?resizew=140)
A.![]() | B.![]() | C.![]() | D.![]() |
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湖北省武汉市新洲区部分学校2023-2024学年高二上学期期中质量检测数学试题江西省吉安市峡江中学2023-2024学年高二上学期期末数学试卷(九省联考题型)(已下线)第3套-复盘卷(已下线)第二章 立体几何中的计算 专题七 空间范围与最值问题 微点3 面积、体积的范围与最值问题(一)【基础版】
4 . 椭圆
:
左右焦点分别为
、
,焦距为2,直线
经过
交椭圆于
两点,若
的周长为12,则椭圆标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3c07ebcbfacda073208d483c58e8a84.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知向量
,
,若
,则实数
等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a4d3e1a98ea05423a864461b97b5a53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31792ebf68a5e9bf066e7d0f4b069987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31c8b7aea9f07e0a3c1543846645d9fb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
A.![]() | B.![]() | C.0 | D.1 |
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解题方法
6 . 已知集合
,
或
,
为实数集.
(1)若
,求实数
的取值范围;
(2)若“
”是“
”的充分不必要条件,且
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92b942eb152e6618620544515936ca78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b30fd68d34698b504304d4cae6a96f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/074a2025262fb224ccab1efd1c8c992b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/343324ebf9d6e86c42fbde0fbb94689d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若“
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ed006b944ea64f970fee46e2f558467.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0eb8c4797efa782ba6d1744e30c9c6eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52854d0ead4737302f4b4706e1f80553.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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湖北省A9高中联盟2023-2024学年高一上学期期中联考数学试卷(已下线)高一上学期期末数学模拟试卷(人教A版2019必修第一册全部)-【题型分类归纳】(人教A版2019必修第一册)河北省保定市第一中学(1+3第八届贯通实验班)2023-2024学年高一上学期第三次阶段测试数学试题(已下线)专题01 与集合与常用逻辑用语有关的参数问题-【寒假自学课】(人教A版2019)
名校
解题方法
7 . 设椭圆
的右焦点为
,直线
与椭圆交于
,
两点,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/538704d01da310c1634587dabff6b356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c43c883a548427f2a895893606e216a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() |
D.当![]() ![]() |
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8 . 吹奏乐器“埙”(如图1)在古代通常是用陶土烧制的,一种埙的外轮廓的上部是半椭圆,下部是半圆.半椭圆
(
,
且为常数)和半圆
组成的曲线D如图2所示,曲线D交
轴的负半轴于点
,交
轴的正半轴于点C,点
是半圆上任意一点,当点
的坐标为
时,
的面积最大,则半椭圆的方程是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc35409c8054fe18431c70e6fea0334.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc65d6eb9b63f96d80b54ec9893aee8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/598e835eed7f949e89c9793353a6a3b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f1f09c3680a6744ab551aa75490da8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dddb32a7a5c157fdf8aa049b2d665b4c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/28/9b3df69e-603e-4f59-befe-bcc327c564c6.png?resizew=217)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知点
在椭圆
上,
,
是椭圆的左、右焦点,若
,且
的面积为1,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/dc7a9140bf7ed15de4241aa9ad8924a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8cc0b4997cae4d8aec791a1d3923314.png)
A.2 | B.![]() | C.2![]() | D.4 |
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解题方法
10 . 已知点
在双曲线
上.
(1)已知点
为双曲线右支上除右顶点外的任意点,证明:点
到
的两条渐近线的距离之积为定值;
(2)已知点
,过点
作动直线
与双曲线右支交于不同的两点
、
,在线段
上取异于点
、
的点
,满足
,证明:点
恒在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be3ad3dd6803d92df6ff8a80cd35095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2702066c515f9b77353cfba5f9e33c0.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f85f1a0c955c915aefe3fcdc9d7eed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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)
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