1 . 已知定点
,动点
满足
,O为坐标原点.
(1)求动点M的轨迹方程
(2)若点B为直线
上一点,过点B作圆M的切线,切点分别为C、D,若
,求点B的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0388d034c4cbfbe51311703b78785430.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5125bf1556f08787ca46f27946055c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8be7da66a28e38acf559aba627cb60bf.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/90603528-5873-4e4b-8513-1226cd67f4b7.png?resizew=220)
(1)求动点M的轨迹方程
(2)若点B为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48d451d8ebfabb3751463a06f0ee986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bd6a2b112facda441f4e34bf5c145fa.png)
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2 . 若关于
的不等式
的解集是
,则
值是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706f92009a05d1eed436f39ef378abe1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e11f4ca0e7ace69f92130d0525bcdb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 已知P是直线l:
上一动点,过点P作圆C:
的两条切线,切点分别为A、B,则四边形PACB的外接圆的面积的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091c83390d0755e1b72755cf37490351.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e18511ccfe2908b100edea1458691fab.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4 . 椭圆
的左右焦点分别为
、
,短轴端点分别为
、
. 若四边形
为正方形,且
.
(1)求椭圆标准方程;
(2)若
、
分别是椭圆长轴左、右端点,动点
满足
,
点在椭圆上,且满足
,求证
定值(
为坐标原点);
(3)在(2)条件下,试问在
轴上是否存在异于
点的定点
,使
,若存在,求
坐标,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfffd420523729074995e9e55f464d4c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71cbb78e8d813953529e8c7156efeb37.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/b1133eee-9265-46aa-8370-c815e316c9f0.png?resizew=200)
(1)求椭圆标准方程;
(2)若
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94e9c33da123d45065865e6c3a8b1a20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3088904983f381dc8856244558f3f0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc6b4cabc5200aa2162915a806ca99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(3)在(2)条件下,试问在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33023f4c86ba1b56ecf3b1dbc84f461a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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5 . 已知矩形
的四个顶点都在椭圆
上,边
和
分别经过椭圆的左、右焦点,且
,则该椭圆的离心率( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56e79f7c3c8815ad1ad3fc8c8d3a50e0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-29更新
|
561次组卷
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2卷引用:安徽省黄山市八校联盟2023-2024学年高二上学期期中考试数学试题
6 . 已知P为圆
上一点,则点
到P点的距离的最大值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95c8fd43588e3d6a8098725ead54ff6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d65d027a85da3f57a3470429f7731a09.png)
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7 . 已知直线
.
(1)若直线l不经过第二象限,求k的取值范围.
(2)若直线l与x轴、y轴正半轴分别交于A、B两点,当△AOB的面积为
时(O为坐标原点),求此时相应的直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35a003a68edc192692dcfee9d2e203b8.png)
(1)若直线l不经过第二象限,求k的取值范围.
(2)若直线l与x轴、y轴正半轴分别交于A、B两点,当△AOB的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c0874f019492261eb175bdcc08c189d.png)
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8 . 在斜三棱柱
中,
,
,
在底面
上的射影恰为
的中点
,又已知
.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/c90ff65e-f009-4f2b-b171-726db9d87ac8.png?resizew=160)
(1)证明:
平面
.
(2)求平面
和平面
的夹角的余弦值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d3a82b8e587ee890467835bc4e854c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/003a97711c5ed89f10594e0aedcabfa8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/209acf15985d1ea1ad86fc4a37e38c0b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2befa96c33901247429a833c46eb193.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/c90ff65e-f009-4f2b-b171-726db9d87ac8.png?resizew=160)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ffc6952e988d04f22f0fb2f7f0ab7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d9a8181f7a7fe7f3fac872ce9534f15.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ef671ff46a372d5351b8c2f9eb26b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9afac7c616bbb14e1ed428a3c507c7dc.png)
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9 . 已知正方体
的棱长为
,
,
分别为
,
的中点,
在直线
上,且
,
的重心为
,则( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/9ee4e46e-a3b5-4ebe-8adb-51aa0a733d03.png?resizew=163)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/394c5d2f55221975503be8aa18022480.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdcf8c5e1133fc3e41c3e181c8584ddf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/9ee4e46e-a3b5-4ebe-8adb-51aa0a733d03.png?resizew=163)
A.若![]() ![]() ![]() | B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() | D.点![]() ![]() ![]() |
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|
123次组卷
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2卷引用:安徽省黄山市屯溪第一中学2023-2024学年高二上学期10月月考数学试题
名校
解题方法
10 . 如图,以棱长为
的正方体的具有公共顶点的三条棱所在直线为坐标轴,建立空间直角坐标系
,点
在体对角线
上运动,点
为棱
的中点,则当
最小时,点
的坐标为( ).
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/16080082-3c84-41be-8ba6-dbbf3e0d6d38.png?resizew=185)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5e336d6ca2cae3d6e6c3810d7e521a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3d87446c9ef0230285d9b08127fce5c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/18/16080082-3c84-41be-8ba6-dbbf3e0d6d38.png?resizew=185)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-12-19更新
|
160次组卷
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4卷引用:安徽省黄山市屯溪第一中学2023-2024学年高二上学期10月月考数学试题
安徽省黄山市屯溪第一中学2023-2024学年高二上学期10月月考数学试题江西省上饶艺术学校2023-2024学年高二上学期期末数学试题(已下线)第6章 空间向量与立体几何单元综合测试卷-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第二册)江苏省扬州市广陵区红桥高级中学2023-2024学年高二下学期3月月考数学试题