名校
1 . 若两圆
和
有公共点,则
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/648c5d95d6085f0c44d8ca9f7d510661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1231a77f60aab1b78faa232249e46fd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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解题方法
2 . 已知椭圆
的焦距与短轴长相等,点
在椭圆上.
(1)求椭圆的标准方程;
(2)已知圆
的切线
与椭圆相交于
两点,证明:以
为直径的圆必经过原点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ad4a60e2b50a820ec2044aa55f2472.png)
(1)求椭圆的标准方程;
(2)已知圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d96d13080edccb0bc63a7218bb0f1404.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2024-01-03更新
|
284次组卷
|
2卷引用:甘肃省白银市靖远县第一中学2023-2024学年高二上学期期末数学模拟卷(一)
名校
解题方法
3 . 设
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f721e5c754e4241ff34591ef0810910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f48402431243ccf5e7e01edd64a0b8c3.png)
A.14 | B.13 | C.12 | D.11 |
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解题方法
4 . 如图,在四棱锥
中,
平面
,四边形
为矩形,M,N分别为
,
的中点,
.
平面
;
(2)求证:平面
平面
.
![](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/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0498b9374bee2169d323c3bd8d2d23d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edcf19a7f0dd0cdf59516ae585025110.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852aabd89edffc1b94344ff3f1f31ccd.png)
(2)求证:平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89571b0ed015bc7533d44b73a74ba309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f747eb5b2d21c9de962cbfd4ec4bb7.png)
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2024-01-02更新
|
370次组卷
|
4卷引用:甘肃省定西市临洮中学2023-2024学年高二上学期第三次质量检测数学试试题
甘肃省定西市临洮中学2023-2024学年高二上学期第三次质量检测数学试试题(已下线)专题8.8 空间中的线面位置关系大题专项训练【七大题型】-举一反三系列湖南省株洲市南方中学2023-2024学年高一下学期期中考试数学试题(已下线)第十一章:立体几何初步章末重点题型复习(2)-同步精品课堂(人教B版2019必修第四册)
名校
解题方法
5 . 在
中,内角A,B,C的对边分别为a,b,c,且满足
.
(1)求C;
(2)若
的面积为
,D为
的中点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4680450786914f54bde2581cdbe16a4.png)
(1)求C;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e4123975f257306440158659634c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
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6 . 已知双曲线
是
上的任意一点.
(1)设点
的坐标为
,求
的最小值;
(2)若
分别为双曲线的左、右焦点,
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c29d3e0290b1cb656ca51fe2a06c8169.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00ed24bfcc37b79fe9ca61ed8fdf26ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7affd8a277498fd39b4a2a95d649f45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
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7 . 已知
.
(1)求直线
的全体方向向量和一个法向量;
(2)若点
在线段
(包括端点)上移动,求直线
的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09cfcccce095dfa2b77f109e699a00a5.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
(2)若点
![](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/03902478df1a55bc99703210bccab910.png)
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解题方法
8 . 如图,在直角坐标系
中,坐标轴将边长为4的正方形
分割成四个小正方形.若大圆为正方形
的外接圆,四个小圆分别为四个小正方形的内切圆,则下列方程是图中某个圆的方程的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/2/40ea9a5f-dacc-4228-9d06-a66b4464f9bc.png?resizew=170)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知椭圆
的左顶点为
,过
作两条互相垂直的直线
且分别与椭圆
交于
两点(异于
点),设直线
的斜率为
,
为坐标原点.
(1)用
表示点
的坐标;
(2)求证:直线
过定点;
(3)求
的面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/893d4e8d70ea2c716ac7b6c1777a77f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)用
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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解题方法
10 . 在平面直角坐标系
中,已知圆
和圆
.
(1)若直线
过原点,且被圆
截得的弦长为6,求直线
的方程;
(2)是否存在点
满足过点
的无穷多对互相垂直的直线
和
,它们分别与圆
和圆
相交,且直线
被圆
截得的弦长与直线
被圆
截得的弦长相等?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9131b2f6321413496907b3ca5ae62ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/132d4325a8e3a7366411bd849cd0d673.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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