名校
解题方法
1 . 已知平面内两个定点
,
及动点
,若
(
且
),则点
的轨迹是圆.后世把这种圆称为阿波罗尼斯圆.已知
,
,直线
,直线
,若
为
,
的交点,则
的最小值为( )
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66525c16a3398262b0fa286f39dd3a56.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e51df6f00d86ca0a579812033a3f7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7368c287ed8f17f8f4b3e5a6dd99042.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d50a53fa7a2bb031e4dce6a51ed3d93.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/560eb37689f5835d1eb01c05b1c4473e.png)
A.3![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2023-02-25更新
|
1539次组卷
|
14卷引用:福建省泉州市2022-2023学年高二上学期期末教学质量监测数学试题
福建省泉州市2022-2023学年高二上学期期末教学质量监测数学试题重庆市涪陵区部分学校2023-2024学年高二上学期第一次月考数学试题(已下线)重难点突破03 直线与圆的综合应用(七大题型)(已下线)第一次月考检测模拟试卷(原卷版)(已下线)第二章 直线与圆的方程(压轴题专练)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)专题05 圆的压轴题(1)(已下线)单元高难问题02数学思想方法在解决与圆有关问题中的应用(各大名校30题专项训练)(原卷版)(已下线)专题02 直线和圆的方程(5)福建省福州教育学院附属中学2023-2024学年高二上学期期末考试数学试题(已下线)圆 与方程(已下线)专题17 圆锥曲线常考压轴小题全归类(16大题型)(练习)(已下线)专题2.1 圆的方程(3个考点九大题型)(2)(已下线)专题2 与圆有关的最值问题【讲】(压轴小题大全)(已下线)专题3 阿波罗尼斯圆及其应用【讲】(压轴小题大全)
2 . 在一个面积为4的直角三角形
的内部作一个正方形,其中正方形的两个顶点落在斜边
上,另外两个顶点分别落在
,
上,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bef5239ddbb0972700ce01daf9ee7cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
A.![]() ![]() | B.![]() |
C.正方形面积的最大值为2 | D.![]() ![]() |
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解题方法
3 . 把底面为椭圆且母线与底面垂直的柱体称为“椭圆柱”.如图,椭圆柱
中底面长轴
,短轴长
,
为下底面椭圆的左右焦点,
为上底面椭圆的右焦点,
,P为
的中点,MN为过点
的下底面的一条动弦(不与AB重合).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/50354766-1f24-49f2-927e-09d1d407e48e.png?resizew=192)
(1)求证:
平面PMN
(2)求三棱锥
的体积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/270ddac9587bf1ea553914cb69595ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a171cc0cc99f030004562afbbc076d31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44d8b20bcb61ee074d884ef80a3c4a99.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7479255f54d51b97e6314db1dc06eb22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6655cc150ddc9deba2254780984d0024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/27/50354766-1f24-49f2-927e-09d1d407e48e.png?resizew=192)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f555e56d727bcfe7c456a58883c5b8a5.png)
(2)求三棱锥
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c259b62bbd2084bfc54723bd85b196f.png)
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2023-02-25更新
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3卷引用:福建省福州市八县(市、区)一中2022-2023学年高二上学期期末联考数学试题
解题方法
4 . 如图,已知一酒杯的内壁是由抛物线旋转形成的抛物面,当放入一个半径为1的玻璃球时,玻璃球可碰到酒杯底部的A点,当放入一个半径为2的玻璃球时,玻璃球不能碰到酒杯底部的A点,则p的取值范围为
您最近一年使用:0次
2023-02-25更新
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7卷引用:福建省福州市八县(市、区)一中2022-2023学年高二上学期期末联考数学试题
福建省福州市八县(市、区)一中2022-2023学年高二上学期期末联考数学试题福建省福州市八县(市)2022-2023学年高二上学期期末联考数学试题(已下线)第三章 圆锥曲线的方程 章末重难点归纳总结-2023-2024学年高二数学《一隅三反》系列(人教A版2019选择性必修第一册)(已下线)第三章 圆锥曲线的方程(易错必刷30题9种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)期末真题必刷压轴60题(23个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)期末真题必刷易错60题(34个考点专练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)(已下线)专题3.3 抛物线(6个考点十大题型)(2)
5 . 已知椭圆
,
的上、下顶点是
,
,左,右顶点是
,
,点
在椭圆
内,点
在椭圆
上,在四边形
中,若
,
,且四边形
面积的最大值为
.
(1)求
的值.
(2)已知直线
交椭圆
于
,
两点,直线
与
交于点
,证明:当
变化时,存在不同于
的定点
,使得
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baff7011784b367fc9bf84e208269240.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e1295b852efee8d6d0a92cbe38439c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e94cea3a50438fdf994c44bb79020a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50639bca2f8b8b4f3db2ec01b1fd2ed6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab8d0b87680432b4b59bde91688b833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e94cea3a50438fdf994c44bb79020a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/303094682b317daea83be885d1c7ff4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/7d0ff310aabd2282b539537ebed3f788.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ec18c028746b73be7503ff6ff458a8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0db06552aa4469859f27f601d5f07536.png)
您最近一年使用:0次
2023-02-14更新
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960次组卷
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3卷引用:湖南省怀化市长沙市长郡中学等3校2023届高三上学期开学考试数学试题
6 . 已知函数
和函数
,关于
的方程
有
个实根,则下列说法中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f33983a78c1a59d7001a175c17fc83ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f0959f324461ddf334f64cf8291554b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cb76acaa0c4670d87aa625ab14d3e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
A.当![]() ![]() | B.当![]() ![]() |
C.![]() ![]() | D.![]() ![]() |
您最近一年使用:0次
名校
7 . 如图,给定外心为
的锐角
,令
分别为
到对边的垂足.
为
的外接圆在
和
处的切线的交点.一条经过
且垂直于
的直线交直线
于
为
在
上的投影.证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80273dbcfcd2fda629a42d425ff25199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e30c0a5c92f50dce1f7624709950ff5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ca00309261a540934d9b3ed9ba05b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95381ea2e4234a389f04150ff11660ef.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/73eec771-3787-4927-b668-78515fb9d732.png?resizew=198)
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8 . 甲、乙两人分别进行投硬币和掷图钉试验,每人各进行100次试验.设
为前k次试验中硬币正面向上的次数,
为前k次试验中图钉针尖朝下的次数,记
.
(1)若
,问是否存在常数P,不论试验过程中
如何变化,均存在某个
,使得
?若存在,求出所有P的可能值;若不存在,请说明理由;
(2)若
,问是否存在常数Q,不论试验过程中
如何变化,均存在某个
,使得
?若存在,求出所有Q的可能值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f255d0395fba51ca2d44293cca42e0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/233427826eb2233641fc3a9805f6d206.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/115e6f9387ea866bc7a9065bb256f855.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae727a3da730ebf0c3e2d6673d7fdb91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe0f61ec213734b7ae080719fa5cdd3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe2b62374f95f9d569a6d5739dda128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f668c772ae36645251661e083ce7f8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98c5596c8546e9600062fea9f799f251.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9778f679a2495d92a52b36e5e86d4b31.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe2b62374f95f9d569a6d5739dda128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46f6d82d629fe8d24b2d8a14a71a8bbf.png)
您最近一年使用:0次
9 . 设点
,过点F作斜率为k的直线l交椭圆
于C,D两点.
(1)记直线
的斜率分别为
.从下列①②③三个式子中任选其一,当k变化时,判断该式子是否为定值,若是,求出定值;若不是,请说明理由.
①
;②
;③
.
(2)当直线
分别交双曲线
的下支于P,Q两点(异于点B)时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20421239f70724807fc2e42f74b1f02d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f182db8ffa0d36588407eae8aeb7aa92.png)
(1)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5913ac8f576f9389802005ae712205d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c65902e35640cf2c8d4111c36b40145.png)
①
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89c20aa9e89d8cc15be390051124ee5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0601dc0a83ff1c3b01dce7cdaa18cabb.png)
(2)当直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2013303974d530fce9a9930938f4c2b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2aea802c49af59b44b8de07f6ef56d90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411e6e928c39bb54f031aa3e5d492852.png)
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解题方法
10 . 设函数
的定义域为I,区间
,如果对于任意的常数
,都存在实数
,满足
,且
,那么称
是区间
上的“绝对差发散函数”.则下列函数是区间
上的“绝对差发散函数”的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/306621a2b3d220bbe34027c1aa503b28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2480f87a11c4cd450bc9454ea7276722.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fe1c31a81f198c443e71b83ca662939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbe1b0b3f9714e1f770d4ca0dca58649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85e86867a0285838dfe2401388d2900d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30277e0be448b4955903e81e8795e45d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab1242ec96ac54e2fd418988d5190a88.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
您最近一年使用:0次