1 . 已知
的其中两个顶点为
,点
为
的重心,边
,
上的两条中线的长度之和为
,记点
的轨迹为曲线
.
(1)求
的方程;
(2)过点
作斜率存在且不为0的直线
与
相交于
两点,过原点
且与直线
垂直的直线
与
相交于
两点,记四边形
的面积为S,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8af2fdf1944afebb51cb6a5e6c74aadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/1dde8112e8eb968fd042418dd632759e.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae3e029070ad0d2ce680d5336ed7150a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58d3ae70ecef31f90e511eba69f99b0c.png)
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2024-04-24更新
|
1016次组卷
|
5卷引用:山东省菏泽市2024届高三下学期模拟预测数学试题(三)
2 . 已知两圆
.一动圆与圆
相外切,与圆
相内切.设动圆的圆心的轨迹为曲线
.
(1)求曲线
的方程;
(2)
为曲线
上的两动点,直线
的斜率为
,直线
的斜率为
,直线
的斜率为
,其中
为
的等比中项,以
为直径的圆的面积为
,以
为直径的圆的面积为
的面积为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f72cc230a8a4d841d0b3db52a64d2f9.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/eec1776bfd268b6b807ac573b4a87ce6.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e56766837f5503b1ee39fb8e05efc924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/531b3540af8141d06802fac03a04cbde.png)
您最近一年使用:0次
2023·全国·模拟预测
名校
解题方法
3 . 已知椭圆C:
的两焦点分别为
,并且经过点
.
(1)求椭圆C的方程;
(2)过
的直线交椭圆C于A,B两点,设直线
与C的另一个交点分别为M,N,记直线AB,MN的倾斜角分别为
,当
取得最大值时,求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5439f5ff9bd5deec0f0ef35c6f605b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a34dda3fc71497fe1a7ef2f3d2c2a953.png)
(1)求椭圆C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0068ae8bb3fb1c75a3843e590fb30607.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e288596fa3811dd2c17bded60e82e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd927b4b5a7875528c1b54aa4bb8b2dd.png)
您最近一年使用:0次
2024-01-02更新
|
442次组卷
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6卷引用:山东省菏泽市2024届高三上学期期末考试数学试题(B)
山东省菏泽市2024届高三上学期期末考试数学试题(B)(已下线)2024年全国高考名校名师联席命制型数学信息卷(七)(已下线)2024年全国高考名校名师联席命制数学(理)信息卷(四)(已下线)2024年全国高考名校名师联席命制数学(文)信息卷(三)江西省上饶市玉山县第二中学2023-2024学年高二上学期12月月考数学试题四川省成都市石室中学2023-2024学年高二上学期期末综合复习数学试题(一)
名校
4 . 已知圆
,圆
,动圆
与圆
外切并与圆
内切,则圆心
的轨迹方程为_______
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d99af3788a5f277a80060c54ae254764.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75fb0a2754d0dcca0537aef3d365f172.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/dad2a36927223bd70f426ba06aea4b45.png)
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2023-08-25更新
|
2019次组卷
|
9卷引用:山东省菏泽市鄄城县第一中学2023-2024学年高二上学期10月月考数学试题
山东省菏泽市鄄城县第一中学2023-2024学年高二上学期10月月考数学试题广东省东莞市第四高级中学2023届高三上学期11月段考数学试题(已下线)2.1.1 椭圆及其标准方程(分层练习)-2023-2024学年高二数学同步精品课堂(北师大版2019选择性必修第一册)(已下线)3.1.1 椭圆及其标准方程(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)考点11 圆锥曲线的定义及其应用(椭圆,双曲线,抛物线) 2024届高考数学考点总动员(已下线)第05讲 椭圆及其性质(八大题型)(讲义)-4(已下线)重难点突破05 求曲线的轨迹方程(十大题型)-1辽宁省朝阳市建平县实验中学2023-2024学年高二上学期期中数学试题(已下线)专题01圆锥曲线中的求方程问题(三大题型)
名校
解题方法
5 . 在平面直角坐标系xOy中,动圆P和圆
:
内切,且与圆
:
外切,记动圆P的圆心轨迹为E.
(1)求轨迹E的方程;
(2)若直线l:
与E交于不同的两点M、N,线段MN的中点记为A,且线段MN的垂直平分线过定点
,求k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e91f4e726059665d140de82d9b105c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae5ce71568a10700c5d9e813fa8e6c49.png)
(1)求轨迹E的方程;
(2)若直线l:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a5464dc3bd349a216296fbaa879ae47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/338d4de5108a28a7ea90a9cda09fea07.png)
您最近一年使用:0次
2022-11-14更新
|
464次组卷
|
3卷引用:山东省菏泽市郓城县郓城第一中学2022-2023学年高二上学期期中数学试题
名校
解题方法
6 . 已知椭圆
的左、右两个焦点分别是F1,F2,焦距为2,点M在椭圆上且满足MF2⊥F1F2,|MF1|=3|MF2|.
(1)求椭圆C的标准方程;
(2)点O为坐标原点,直线l与椭圆C交于A,B两点,且OA⊥OB,证明
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)求椭圆C的标准方程;
(2)点O为坐标原点,直线l与椭圆C交于A,B两点,且OA⊥OB,证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acb8956ebcde7cf0f1011a2fc1888e15.png)
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2022-12-09更新
|
590次组卷
|
6卷引用:山东省菏泽市2022-2023学年高二上学期期末数学试题
山东省菏泽市2022-2023学年高二上学期期末数学试题河南省平顶山市2020-2021学年高二上学期期末数学(理)试题河南省平顶山市2020-2021学年高二上学期期末数学(文)试题(已下线)第42讲 解析几何中的长度之和差积商平方问题-2022年新高考数学二轮专题突破精练河南省安阳市第一中学2020-2021学年高二上学期期末测试文科数学试题河南省信阳市商城县观庙高级中学2021-2022学年高二上学期12月月考数学(理)试题
名校
7 . 方程
化简的结果是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b57af08404fd307ec4f8a25a62f7b3cf.png)
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2022-03-16更新
|
1061次组卷
|
5卷引用:山东省菏泽市山大附中实验学校2022-2023学年高二上学期第二次阶段测试数学试题
山东省菏泽市山大附中实验学校2022-2023学年高二上学期第二次阶段测试数学试题安徽省蚌埠第三中学2021-2022学年高二下学期开学测试数学试题(已下线)第13讲 椭圆(1)(已下线)第05讲 椭圆 (精讲)-1(已下线)第三章 圆锥曲线的方程(A卷·知识通关练)(1)
8 . 已知
中,
,
,
,
,曲线E过C点,动点Р在E上运动,且保持
的值不变.
(1)求曲线E的方程;
(2)过点
的直线
与曲线
交于M,N两点,则在
轴上是否存在定点
,使得
的值为定值?若存在,求出点
的坐标和该定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f8f88798ec42a58dccd212586382b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c10d461a7c0b86a2f09c2ea17f38260e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be4b1309e4a2d8c1dc092ef78d09f3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
(1)求曲线E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f78d33e95e9a27695947a489ae3bf1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
您最近一年使用:0次
2022-02-13更新
|
431次组卷
|
2卷引用:山东省菏泽市2021-2022学年高三上学期期末数学试题
9 . 如图,已知圆
:
,点
是圆
内一个定点,点
是圆上任意一点,线段
的垂直平分线
和半径
相交于点
.当点
在圆上运动时,点
的轨迹为曲线
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/e5739b5a-44f3-42ae-81ff-dd209b92224f.png?resizew=140)
(1)求曲线
的方程;
(2)设过点
的直线
与曲线
相交于
两点(点
在
两点之间).是否存在直线
使得
?若存在,求直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a8dfa9c643db95f387916f715d1a846.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cdba1337ec85fa9722cb4b320a82ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/e5739b5a-44f3-42ae-81ff-dd209b92224f.png?resizew=140)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fb203d8908ffd00fc19e6d8b5f3eae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b930eaaa7f71103e63f1d56b36aa970f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06db0d2968d2128cb4d5a8e40981d671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
您最近一年使用:0次
2020-01-29更新
|
3680次组卷
|
11卷引用:山东省菏泽市成武一中2020届高三数学第二次模拟试题
山东省菏泽市成武一中2020届高三数学第二次模拟试题广东省广州市荔湾区2019-2020学年高二上学期期末数学试题(已下线)必刷卷08-2020年高考数学必刷试卷(新高考)【学科网名师堂】-《2020年新高考政策解读与配套资源》广东省广州市八区2019-2020学年高二上学期期末教学质量监测数学试题广东省广州市白云区2019-2020学年高二上学期期末教学质量检测数学试题(已下线)卷08-2020年高考数学冲刺逆袭必备卷(山东、海南专用)【学科网名师堂】(已下线)专题06 平面向量在解析几何中的应用(第五篇)-2020高考数学压轴题命题区间探究与突破广东省广州市海珠区2019-2020学年高二上学期期末联考数学试题(已下线)重难点04 解析几何-2021年高考数学【热点·重点·难点】专练(新高考)(已下线)专题04 平面向量-【备战高考】2021年高三数学高考复习刷题宝典(压轴题专练)(已下线)专题1 解析几何与平面向量
10 . 已知圆
,圆心为点
,点
是圆
内一个定点,
是圆上任意一点,线段
的垂直平分线
和半径
相交于点
在圆上运动.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/2d24f6ba-6fc4-4d8b-9b4e-82a97e9ca5ad.png?resizew=159)
(l)求动点
的轨迹
的方程;
(2)若
为曲线
上任意一点,
|的最大值;
(3)经过点
且斜率为
的直线交曲线
于
两点在
轴上是否存在定点
,使得
恒成立?若存在,求出点
坐标:若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d038b9cfe480f5367391030cb07440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a98eaaab44a91d0bad21dbd260be770.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63a253c7fdf589ee3dece13d5b5b5732.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883147d5e14285f65184f8a75de14221.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/17/2d24f6ba-6fc4-4d8b-9b4e-82a97e9ca5ad.png?resizew=159)
(l)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/229f8fee65d62506665a770192fb4361.png)
(3)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c0878af1501b3447c5dc33758fd290b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d70de1ffdd9aa376b09bbcfa12644a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba6750bb8fef3bfe7fc30b5aba148ff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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