名校
1 . 已知集合
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a30ff913a6547cbc197d3cb81f2caa19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-20更新
|
600次组卷
|
2卷引用:安徽省黄山市黄山学校2023-2024学年高一上学期期末模拟数学试题(一)
2 . 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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解题方法
3 . 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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4 . 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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5 . 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)
您最近一年使用:0次
6 . 已知
,
,
,
是实数,则下列说法错误的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() ![]() |
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解题方法
7 . 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
|
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
8 . 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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解题方法
9 . 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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名校
10 . “绿水青山就是金山银山”,为了贯彻落实习近平生态文明思想,探索促进“绿水青山”向“金山银山”转变的重大实践,某地林业局准备围建一个矩形场地,建立绿化生态系统研究片区,观察某种绿化植物.如图所示,两块完全相同的矩形种植绿草坪,草坪周围(阴影部分)均种植宽度相同的花,已知两块矩形绿草坪的面积均为
平方米,共
平方米.
![](https://img.xkw.com/dksih/QBM/2023/12/19/3392568616009728/3392634341875712/STEM/79c0b178f11d4cc9bf89181dab7d50f8.png?resizew=129)
(1)若矩形草坪的长比宽至少多
米,求草坪宽的最大值;
(2)若草坪四周的花坛宽度均为
米,求整个绿化面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b685c556cc423e4833c1dc671a134cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98ac61206cb12cf6686bb0facf635010.png)
![](https://img.xkw.com/dksih/QBM/2023/12/19/3392568616009728/3392634341875712/STEM/79c0b178f11d4cc9bf89181dab7d50f8.png?resizew=129)
(1)若矩形草坪的长比宽至少多
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d91e07104b699c4012be2d26160976a2.png)
(2)若草坪四周的花坛宽度均为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
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