名校
解题方法
1 . 已知圆心为C的圆经过点
和
,且圆心C在直线
上,
(1)求圆C的标准方程.
(2)过点
作圆的切线,求切线方程
(3)求x轴被圆所截得的弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf5a6145990adf5574f0e0f2fc828ea4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6419152065edb8cabf887b65adb4a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
(1)求圆C的标准方程.
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86b85acb5a868b0ff2a17b1ca926dd43.png)
(3)求x轴被圆所截得的弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
名校
解题方法
2 . 已知椭圆
(
)的长轴长是短轴长的2倍.
(1)求椭圆的离心率
;
(2)直线
过点
且与椭圆有唯一公共点
,
为坐标原点,当
的面积最大时,求椭圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
(1)求椭圆的离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c41b2f7ca11db3aaea46c69286adbce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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4卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
名校
解题方法
3 . 已知双曲线
(
,
)的左右焦点分别为
,
,过
的直线
与圆
:
相切,与双曲线在第四象限交于一点
,且有
轴,则离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.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/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85a3c31a3ee596913d198aae09cd0a77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce9a7ab181883910f06f7fbecc6ea25d.png)
A.3 | B.![]() | C.![]() | D.2 |
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2卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
名校
4 . 已知点
,
,点C为圆
上一点,则
的面积的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1aacade1de64210bb11fa0dfe6c4343b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
A.12 | B.![]() | C.![]() | D.6 |
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3卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
天津市东丽区2023-2024学年高二上学期期中数学试题天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题(已下线)2.4.2 圆的一般方程【第二练】“上好三节课,做好三套题“高中数学素养晋级之路
名校
解题方法
5 . 如图,
平面
,
,
,
,
,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805f923318ab818c77ad9b767a2af065.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/7cc0da43-8e5e-47cf-9c2f-51f585d3ca98.png?resizew=171)
(1)求证:
平面
;
(2)求平面
与平面
夹角的余弦值;
(3)求点
到平面
的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f4c3f9dd5d0343597a7f58a1989b537.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9060f03b9ee41d70d135b1e1a8902ce9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05e952f7b05d06917128bfecb64fe3cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f571396be1aa4a8914a66f7d7abd6381.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f04ab8b50f9e76c5fa2a0c3b5c1debf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/805f923318ab818c77ad9b767a2af065.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/19/7cc0da43-8e5e-47cf-9c2f-51f585d3ca98.png?resizew=171)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a5928c98b341b16d4b5a5b931d2929d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
(2)求平面
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a09d9d486b7f91ba933210dd013a7f2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
(3)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f636f76d550dfb593a25eb680cff556.png)
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4卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
名校
6 . 与椭圆C:
共焦点且过点
的双曲线的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e78f1a9cc4dedc05c175ab99b288b9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5f4493abd2b69f83eae0362c509f1a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
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7 . 已知抛物线C:
的焦点为F,O为原点,点M是抛物线C准线上的一动点,点A在抛物线C上,且
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42102c1c07562853219ca5918803a27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5ba3a6326dc83632fa772c1d34cbff9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a763d5699555f45f789347f03502c64e.png)
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8卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
天津市东丽区2023-2024学年高二上学期期中数学试题天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题天津市北辰区南仓中学2023-2024学年高二上学期第二次月考数学试题北京市陈经纶中学2023-2024学年高二上学期12月月考数学试题(已下线)3.3.1 抛物线及其标准方程(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)(已下线)3.3.1 抛物线的标准方程(5大题型)-【题型分类归纳】2023-2024学年高二数学同步讲与练(苏教版2019选择性必修第一册)(已下线)专题03 圆锥曲线方程(2)天津市北师大静海实验学校2023-2024学年高二上学期第三次月考数学试题
名校
8 . 如图,在三棱锥
中,
底面
,
,点D,E,N分别为棱
,
,
的中点,M是线段
的中点,
,
.
平面
;
(2)求直线
与平面
所成角的正弦值;
(3)已知点H在棱
上,且直线
与直线
所成角的余弦值为
,求线段
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63397cda22cb1fad59cf966dfb588643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccd4fd4b7a4d6b8ca0c5827c055a9ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c06154cae3bf7a8ce5a1e97a7380875.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00bab2c27eac56fffa4cd7dbe1dcdf1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3e9ef3e849788645552cfb0735d987.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7592c4f01c8e06c7ee90df5b9413a9f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(2)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eedae8d316c76e3d0b451256de03fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
(3)已知点H在棱
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff9d2abf13c2842f58654abf73c6b4ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d86ab7c97cd8a0b15ba5efc1be94230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/826c728050e3378921442ace20269ef6.png)
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4卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
名校
解题方法
9 . 过点
的直线与椭圆
交于A、B两点,且满足
.若M为直线
上任意一点,O为坐标原点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc210625e54a64a625eaa3dbf841c9f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc2518c64be54c16908f868034d8fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab28821e5d304dae10bce5aac560c8b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c19fa4cd646f4d877c3e58cc346651.png)
A.1 | B.![]() | C.2 | D.![]() |
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4卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题
天津市东丽区2023-2024学年高二上学期期中数学试题天津市第一百中学、咸水沽第一中学2023-2024学年高二上学期期中联考数学试题(已下线)专题16 椭圆的中点弦问题(期末选择题16)2023-2024学年高二数学上学期期末题型秒杀技巧及专项练习(人教A版2019)(已下线)期末测试卷01(测试范围:第1-4章数列)-2023-2024学年高二数学《重难点题型·高分突破》(人教A版2019选择性必修第二册)
名校
解题方法
10 . 设椭圆
(
)的左右焦点分别为
,
,左右顶点分别为A,B,
,
.
(1)求椭圆的方程;
(2)已知P为椭圆上一动点(不与端点重合),直线
交y轴于点Q,O为坐标原点,若四边形
与三角形
的面积之比为
,求点P坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/a2644e9f73e5871db934fdafc431d675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5de403dabee36d6ae22acc9df4fab3d.png)
(1)求椭圆的方程;
(2)已知P为椭圆上一动点(不与端点重合),直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a4fda3a965fce9123708bab73c1f2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bd9c299d7ed6e96cd09cae67d7bba41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b1dcdac71e394e495d069f64e1f1ce9.png)
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5卷引用:天津市东丽区2023-2024学年高二上学期期中数学试题