名校
解题方法
1 . 已知椭圆
:
的离心率为
,其左、右焦点为
、
,过
作不与
轴重合的直线
交椭圆
于
、
两点,
的周长为8.
(1)求椭圆
的方程;
(2)设线段
的垂直平分线
交
轴于点
,是否存在实数
,使得
?若存在,求出
的值;若不存在,请说明理由.
(3)以
为圆心4为半径作圆,过
作直线
交圆
于
、
两点,求四边形
的面积的最小值及取得最小值时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.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/81dea63b8ce3e51adf66cf7b9982a248.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76ea1c3fe8431260ecb8dffcdae8d570.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/27/41338274-ca1d-4cfd-99fa-8b0a858f3b31.png?resizew=202)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b786a819ee6702edfc2fa26123e98ed9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
(3)以
![](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/73914b8189da50ca10a629b52010f9eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.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/ae3e029070ad0d2ce680d5336ed7150a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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5卷引用:浙江省衢温“5+1”联盟2022-2023学年高二上学期期中联考数学试题
浙江省衢温“5+1”联盟2022-2023学年高二上学期期中联考数学试题广东五校2022-2023学年高二下学期期末联考数学试题江苏省扬州市邗江区邗江中学2023-2024学年高二上学期期中数学试题(已下线)专题突破卷23 圆锥曲线大题归类(已下线)重难专攻(十一)?圆锥曲线中的证明,探究性问题(核心考点集训)
名校
解题方法
2 . 如图,若正方体的棱长为2,点
是正方体
的底面
上的一个动点(含边界),
是棱
的中点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e09725691ee7851f54c0dee86b2bf55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632f2bf1cd0435041fa04b01901d1c8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d88bf46ad08f9677c37eed1d0369329.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/28/b8fdaf1a-be9f-4764-8968-755fa3265c06.png?resizew=173)
A.若保持![]() ![]() ![]() ![]() |
B.三棱锥![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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2卷引用:浙江省衢温“5+1”联盟2022-2023学年高二上学期期中联考数学试题
3 . 已知函数
,
的导函数为
.
(1)若
存在极值点,求
的取值范围;
(2)设
的最小值为
,
的最小值为
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9555cadc1cf24ddeabc67519ef89eb82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4669810732b633b60dbeaf0bf57204f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6a24198bd04c29321ae5dc5a28fe421.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45c2f5c97fe0a54376065c21a52695bb.png)
您最近一年使用:0次
名校
4 . 已知函数
,若不等式
对
恒成立,则实数a的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b734c10d04d1129de6542284763eb6dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8fab10472cd59dcfe92297f3c355b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08115d6d9f876dea921a4d32260ff1fb.png)
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|
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6卷引用:浙江省9+1高中联盟2022-2023学年高二下学期期中数学试题
浙江省9+1高中联盟2022-2023学年高二下学期期中数学试题(已下线)【2023】【高二下】【期中考】【367】【高中数学】【马定超收集】广东省广州市2023届高三冲刺(一)数学试题湖南省常德市第一中学2023-2024学年高三上学期第二次月考数学试题湖南省2024届高三数学新改革适应性训练二(九省联考题型)(已下线)专题11 不等式恒成立、能成立、恰好成立问题(过关集训)
名校
解题方法
5 . 为了保证我国东海油气田海域的海上平台的生产安全,海事部门在某平台
的正东方向设立了两个观测站
和
(点
在点
、点
之间),它们到平台
的距离分别为1海里和4海里,记海平面上到两观测站的距离
之比为
的点
的轨迹为曲线
,规定曲线
及其内部区域为安全预警区(如图).
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/948d0c6d-163e-4c6d-b7f1-78a64065801e.png?resizew=169)
(1)以
为坐标原点,1海里为单位长度,
所在直线为
轴,建立平面直角坐标系,求曲线
的方程;
(2)海平面上有巡航观察点
可以在过点
垂直于
的直线
上运动.
(i)若
为
的中点,求
的最小值;
(ii)过
作直线
与曲线
相切于点
.证明:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b8b34852ec6aec5e4232ed35dfa2557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/12/948d0c6d-163e-4c6d-b7f1-78a64065801e.png?resizew=169)
(1)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)海平面上有巡航观察点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(i)若
![](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/b3be176992c5f430469028c0506cd084.png)
(ii)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63414dc4bac8ce524634b84b43dd8fcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
6 . 已知圆
,圆上有一动点P,线段PF的中垂线与线段PE交于点Q,记点Q的轨迹为C.第一象限有一点M在曲线C上,满足
轴,一条动直线与曲线C交于A、B两点,且直线MA与直线MB的斜率乘积为
.
(1)求曲线C的方程;
(2)当直线AB与圆E相交所成的弦长最短时,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d980af5cd3091bdfbbd5a2a47c0595d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7e98fa4da2def9eebd11a349b83e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1a28d07fb1904c65774987073d6f9d.png)
(1)求曲线C的方程;
(2)当直线AB与圆E相交所成的弦长最短时,求直线AB的方程.
您最近一年使用:0次
2023-09-04更新
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5卷引用:浙江省七彩阳光联盟2022-2023学年高二上学期期中数学试题
浙江省七彩阳光联盟2022-2023学年高二上学期期中数学试题福建省厦门第二中学2022-2023学年高二上学期第二次阶段考(12月)数学试题(已下线)专题03 圆锥曲线的方程(3)重庆市四川外语学院重庆第二外国语学校2024届高三上学期九月测试数学试题(已下线)考点18 解析几何中的范围、最值问题 2024届高考数学考点总动员【练】
名校
解题方法
7 . 三支不同的曲线
交抛物线
于点
,
为抛物线的焦点,记
的面积为
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c042b615c2efdb8e88e33f0b03e59b68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b4cdf33ab57e5c1de20bd4707df69dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0a4eaa5f726407d4dc0d38150b56545.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e9bb415ebf91617fe843b83d0a140ea.png)
A.![]() | B.![]() |
C.若![]() ![]() | D.若![]() ![]() |
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3卷引用:浙江省台州市第一中学2023-2024学年高二上学期期中数学试题
名校
8 . 已知函数
.
(1)若
,
,求实数a的取值范围;
(2)设
是函数
的两个极值点,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16cc71eacaec8e1aaeffec91d19518fa.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fde64f4d3c38e43fbdee24eadc4b0dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/018857ec6e498113b3b12a730d9313da.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce7ae90d808f05e86ea063238e4b2f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fe7d5809da02c15a43a0e9a898b9086.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ebc1d8bb31485daaab989fb4368db6eb.png)
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8卷引用:浙江省宁波市余姚中学2023-2024学年高二上学期第一次质量检测数学试题
浙江省宁波市余姚中学2023-2024学年高二上学期第一次质量检测数学试题江苏省南京市金陵中学2022-2023学年高二下学期期末数学试题江苏省八市(南通、泰州、扬州、徐州、淮安、连云港、宿迁、盐城)2023届高三二模数学试题(已下线)押新高考第22题 导数综合解答题(已下线)江苏省八市2023届高三二模数学试题变式题17-22专题07导数及其应用(解答题)江苏省八市2023届高三下学期第二次调研测试数学试题四川省宜宾市第六中学校2024届高三上学期期末数学(理)试题
名校
9 . 已知
.
(1)证明:当
时,
在
上单调递增;
(2)当
时,关于
的不等式
在
上恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a95afb3cd057b52806817966e6ccd2b.png)
(1)证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb5f421939ee855f25927e7570d82c71.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09f86f37ec8e15846bd731ab4fcdbacd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/917ae6fcf56fa6b4fc9852854cd8f78b.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b550ee821ee1838384835e81fc34b67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb89b43d34a805025b439f6aabb15529.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0bb82965d5b3c7426b5fc82f5edeb7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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8卷引用:浙江省宁波市北仑中学2022-2023学年高二(1班)下学期期中数学试题
10 . 已知椭圆
的左、右顶点分别为
,
,点
在椭圆C上,且
的面积为3.
(1)求椭圆
的方程;
(2)设直线
不经过点
且与椭圆
交于
两点,若直线
与直线
的斜率之积为
,作
于
点.
①求证:直线
过定点,并求出定点的坐标;
②问是否存在定点
,使得
为定值?若存在,请求出该定值,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/a0dfb290b1a84f670549554a0c988593.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b4f4499c0501fd24a9d66e3c97b9038.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a431edd18debb185c471b0efd95ed171.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②问是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e42887d9bf31c1dd99f13c39e63c9ab9.png)
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