名校
解题方法
1 . 已知双曲线
的右焦点为F,点
分别为双曲线C的左、右顶点,过点F的直线l交双曲线的右支于
两点,设直线
的斜率分别为
,且
.
(1)求双曲线C的方程;
(2)当点P在第一象限,且
时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/222b4c3088d36ba0b2f5d8dedbcfc902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378f90fe1e622bab7a8fb2ccdc0c11cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b8bfb1960c394ccfb7bb12de1c1b2b.png)
(1)求双曲线C的方程;
(2)当点P在第一象限,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec79607071014df4522d49f117583c42.png)
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10卷引用:山西省晋中市晋中新格伦双语学校等2校2022-2023学年高三上学期12月月考文数试题
山西省晋中市晋中新格伦双语学校等2校2022-2023学年高三上学期12月月考文数试题河南省百师联盟2023届高三一轮复习联考(四)全国卷理科数学试题云南省马关县第一中学2023届高三第七次月考数学试题江苏省宿迁市沭阳塘沟高级中学2022-2023学年高二下学期第一次月考数学试题(已下线)仿真演练综合能力测试(二)辽宁省锦州市渤海大学附属高级中学2022-2023学年高三上学期期末考试数学试题辽宁省盘锦市高级中学2022-2023学年高三下学期第一次模拟考试数学试题云南省陆良县第八中学2023届高三上学期期末数学试题云南省昆明市西山区2022-2023学年高二上学期2月期末考试数学试题江苏省无锡市南菁高级中学2023-2024学年高二上学期期末模拟数学试题
名校
2 . 双曲线C:
的左,右焦点分别为
,
,过
的直线与C交于A,B两点,且
,
,点M为线段
的中点,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3040b6c904477030ecf8ba20b2b18759.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3a7681c38f74e21181bb9de077b0c0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6a4ebe4e7f13e979ac94a3b4904af4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd12cd3cc9732627d3115abb76d55d9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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4卷引用:河南省(菁师联盟)2022-2023学年高三上学期12月质量监测考试理科数学试题
名校
解题方法
3 . 已知在
中,角
所对的三边分别为
,
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24e0c10fb103930eabd5fa18e8f9bb06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76f0649064a085fb74c997fb507a9b6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe29c42302504e7fd8577dbc7d130ac7.png)
A.若![]() ![]() |
B.若![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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3卷引用:2023届西南3+3+3高考备考诊断性联考(一)数学试题
4 . 已知函数
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffa402121acb4a485415ff8af940d0f.png)
A.![]() ![]() |
B.![]() ![]() |
C.![]() ![]() |
D.![]() ![]() |
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2卷引用:辽宁省辽阳市2022-2023学年高三上学期12月月考数学试题
名校
解题方法
5 . 在
中,
,
,
,点
在该三角形的内切圆上运动,若
(
,
为实数),则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d2c15801fee2405573677484f5dcfa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f8eeeea1c9652cacce976f8129cf520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/267880e605306851d8f46be77b11f9c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db121ef04468ca96f9605ea4d89d6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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|
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3卷引用:江苏省G4联盟(苏州中学、扬州中学、盐城中学、常州中学)2022-2023学年高三上学期12月联考数学试题
江苏省G4联盟(苏州中学、扬州中学、盐城中学、常州中学)2022-2023学年高三上学期12月联考数学试题广西壮族自治区钦州市第四中学2023届高三上学期12月考试数学(?理)试题(已下线)【讲】专题五 平面向量的综合问题(压轴大全)
6 . 在
中,
,
于D,点E在线段
上,点
关于直线
的对称点分别为
,则
的面积的最大值为___ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/183c6568b2466499cd4413c8b99014f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5f215a42c4b7078d8d65923eb9980e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab609a6574633ebabcff3e73fa862081.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64225c1c0fbf186da0987d102b03d14c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80f6f541cf6929fc899ddc37289bf3d1.png)
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名校
7 . 已知定义在
上的函数
是偶函数,当
时,
,若关于
的方程
,有且仅有6个不同实数根,则实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf3ed15aa3dcc4211fb520b5b942c989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/942c2141d01bde6b48210c56a17fc75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6e2e79843faf62dde86bf858d1e0569.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a465e9b24a98fb492d32fdec018094e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f9213787f50b9bbecae4bb26c2284bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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|
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|
3卷引用:广西桂林市第五中学2023届高三上学期11月月考数学(文)试题
名校
解题方法
8 . 已知
为椭圆
上不同的三点,直线
,直线
交
于点
,直线
交
于点
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/388dafb140991d8b379cb0c00e7d6316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf37fb661ccc2fdd67407269708df4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbd8a5d973b7a54b7605388fdcfbb07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.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/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9eb9842cc08baeb0df13fd047fdb79d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bffd29b2e8192d673308bdf8d5cb6cab.png)
A.0 | B.![]() | C.![]() | D.![]() |
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10卷引用:江苏省扬州中学2022-2023学年高二上学期12月月考数学试题
江苏省扬州中学2022-2023学年高二上学期12月月考数学试题浙江省台金六校2022-2023学年高二上学期期中联考数学试题福建省三校联考2022-2023学年高二上学期期中考试数学试题重庆市第八中学校2023-2024学年高二上学期定时检测(四)数学试题浙江省宁波市鄞州中学2023-2024学年高二上学期9月月考数学试题河北省邯郸市魏县2022-2023学年高二上学期期末考试数学试题浙江省杭州市源清中学2022-2023学年高二上学期期末数学试题辽宁省沈阳市东北育才学校2023届高三高考适应性测试(二)数学试题(已下线)第五节 椭圆 第二课时 直线与椭圆的位置关系 B素养提升卷(已下线)专题12 椭圆-2
解题方法
9 . 已知椭圆
:
(
)的左、右顶点分别
,
,上顶点为
,
,
的长轴长比短轴长大6.
(1)求椭圆
的方程;
(2)斜率不为0的直线
交
于
,
两点(异于点
),且
,证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25542d512877cec6713c102ccef241f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率不为0的直线
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddd5be522eacb5ca13c1c483a9e9a932.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
10 . 如图所示,
,
是双曲线
:
(
,
)的左、右焦点,
的右支上存在一点
满足
,
与
的左支的交点
满足
,则双曲线
的离心率为( )
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a721d045-d95c-4618-b19d-6df9b19d4778.png?resizew=164)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce85c3ebf44fbb0a5fcd53d65fd6082.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5b427dafbdbddf66eb5ebc168b10e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/26/a721d045-d95c-4618-b19d-6df9b19d4778.png?resizew=164)
A.3 | B.![]() | C.![]() | D.![]() |
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9卷引用:江西省西路片七校2023届高三上学期第一次联考数学(文)试题