名校
1 . 在平面直角坐标系
中,动圆
与圆
:
内切,且与圆
:
外切,记动圆
的圆心的轨迹为
.
(1)求轨迹
的方程;
(2)已知
分别为轨迹
的左、右顶点,点
不与
重合.直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
与直线
交于点
,
与
轴交于点
,直线
与直线
的交点为
,若四点
共圆.求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求轨迹
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a461995b90655f5133df6f61c2d09bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6f7b16d65f1b2b8bea8cf4a83fde925.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3ca78154dab846367fabbe29abed277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
名校
解题方法
2 . 已知中心在原点,长轴在
轴上的椭圆
的左右顶点分别为
和
,P为椭圆上的除左右顶点外的任一点,且
,
斜率之乘积为
.
(1)求椭圆
的方程;
(2)过
分别作两条直线与椭圆
交于点
,点
;线段
的中点为
,线段
的中点为
,若
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/046f519bdb2972cf7d2f2377c6398b54.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40540618c5b9bb0de570d4c742efe648.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f30d314a642667fef559032264647366.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c0b06dc01c30d13f64be2ac6a1d811e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
3 . 在平面直角坐标系
中,点
,点
是平面内的动点.若以PF为直径的圆与圆
内切,记点P的轨迹为曲线E.
(1)求E的方程;
(2)设点
,
,
,直线AM,AN分别与曲线E交于点S,T(S,T异于A),
,垂足为H,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46542271c7fa06f33b222424838c9684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
(1)求E的方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b10c64cc584dde9a132ab54c6981cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e59cc6019966ce25e3ad146e992f0c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c60030f98d7cf695840770c05e63dbd1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a31666076b1d37cd2f99afa950da5ab.png)
您最近一年使用:0次
2023-12-18更新
|
1753次组卷
|
5卷引用:湖南省长沙市长郡中学2024届高三上学期期末适应性考数学试题
湖南省长沙市长郡中学2024届高三上学期期末适应性考数学试题(已下线)模块一 专题2 《解析几何》单元检测篇 B提升卷广东省广州市2024届高三上学期调研测试数学试题(B)(已下线)专题11椭圆(3个知识点7个拓展2个突破7种题型2个易错点)-【倍速学习法】2023-2024学年高二数学核心知识点与常见题型通关讲解练(人教A版2019选修第一册)重庆市南开中学校2023-2024学年高二下学期阶段测试数学试题
名校
解题方法
4 . 已知椭圆
离心率
,设点M和N分别是椭圆上不同的两动点.
(1)求椭圆C的标准方程;
(2)若直线MN过点
,且
,线段MN的中点为P,求直线OP的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee76e9637ea9efd96e55d208c754b44f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
(1)求椭圆C的标准方程;
(2)若直线MN过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cd48cdef1cbc81392acd38a6cad6530.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa5765c67e2ee7ddc0935328319ec5c0.png)
您最近一年使用:0次
2023-11-25更新
|
705次组卷
|
3卷引用:湖南省长沙市明德中学2023-2024学年高二上学期期末考试数学试卷
名校
解题方法
5 . 在平面直角坐标系
中,已知椭圆C:
(
)的左、右焦点分别为
,且焦距为
,椭圆C的上顶点为B,且
.
(1)求椭圆C的方程;
(2)若直线l过点
,且与椭圆C交于M,N两点(不与B重合),直线BM与直线BN分别交直线
于P,Q两点.判断是否存在定点G,使得点P,Q关于点G对称,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ea617baa0c3518c68a4ba38a66d4269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18e78e65b66230c8ccb7193ac69ffc85.png)
(1)求椭圆C的方程;
(2)若直线l过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06ebd2da016e7029c4dd72b9e377190c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
您最近一年使用:0次
2023-11-23更新
|
354次组卷
|
4卷引用:湖南省长沙市长沙县省示范学校2023-2024学年高二上学期期末检测数学试题
名校
解题方法
6 . 已知椭圆
经过点
,且离心率为
.
(1)求椭圆E的方程;
(2)若经过点
,且斜率为k的直线与椭圆E交于不同的两点P,Q(均异于点A),证明:直线AP与AQ的斜率之和为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆E的方程;
(2)若经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0f9f734c03d04c21edefa08e0acc1fa.png)
您最近一年使用:0次
2023-07-06更新
|
2108次组卷
|
8卷引用:湖南省长沙市第一中学2022-2023学年高二下学期期末数学试题
湖南省长沙市第一中学2022-2023学年高二下学期期末数学试题河南省平顶山市2022-2023学年高二下学期期末数学试题(已下线)模块三 专题6 大题分类练(圆锥曲线)基础夯实练 期末终极研习室(高二人教A版)(已下线)第20讲 椭圆的简单几何性质10种常见考法归类(2)(已下线)模块四 专题6 暑期结束综合检测6(能力卷)(已下线)第02讲 3.1.2椭圆的简单几何性质(2)(已下线)3.1.2 椭圆的几何性质(2)(已下线)专题03 椭圆13种常见考法归类(2)
7 . 已知椭圆C:
,
,
为椭圆C的左、右顶点,
,
为左、右焦点,Q为椭圆C上任意一点.
(1)求直线
和
的斜率之积;
(2)直线l交椭圆C于点M,N两点(l不过点
),直线
与直线
的斜率分别是
,
且
,直线
和直线
交于点
.
①探究直线l是否过定点,若过定点求出该点坐标,若不过定点请说明理由;
②证明:
为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3853a47e9138f78e83786b0d6e85bce4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f387b16cc48e57112c89c8af2a90c1d6.png)
(2)直线l交椭圆C于点M,N两点(l不过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448eb7d301baa90fe59b05761830f81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a439c8a01a6626d7a3f53af31ef0bcae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78bb56032b37aaf40bfbac51f7fe2d9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b06b75fb4e379ff3b99e68f40136cad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
①探究直线l是否过定点,若过定点求出该点坐标,若不过定点请说明理由;
②证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
2023-02-15更新
|
800次组卷
|
4卷引用:湖南师范大学附属中学2022-2023学年高二上学期期末数学试题
名校
解题方法
8 . 设F,E分别是椭圆
的左,右焦点,椭圆上存在点N,满足
且
的面积为20.
(1)求b的值;
(2)设点P的坐标为
,直线过点P,与椭圆交于点A,B,线段
的中点记为M.若
是
与
的等比中项,求a的最小值,并求出此时直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d71528844499d541fb06d16147a1cf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a35a55ff4c434ce34d90382cea5afb85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08fffabcb0a245d00182082c8cc99349.png)
(1)求b的值;
(2)设点P的坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c832f2474efe89961ef41e884da7660c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cb79ed88746f9163c7c6b0b674556de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4522fdddbca40f55f3130c4c44e0bb62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03e944586ad3d14e01f4d1ad9d8f4910.png)
您最近一年使用:0次
名校
9 . 已知椭圆
:
(
)过点
,过右焦点
且垂直于x轴的直线交椭圆C于
、
两点,且
,
为坐标原点.
(1)求椭圆C的方程;
(2)若过原点的直线
与椭圆C交于
、
两点,且在直线
:
上存在点
,使得
为等边三角形,求直线
的方程.
![](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/df31c675af44a719b896de0f4bb163db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/dd8f669605b372b245fd7c05074ba3a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆C的方程;
(2)若过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.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/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbf995182e759c6c6e8eed079274293.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
您最近一年使用:0次
2022-01-13更新
|
385次组卷
|
3卷引用:湖南省长沙市第一中学2020-2021学年高二上学期期末数学试题
解题方法
10 . 设椭圆C:
(
)的离心率为
,焦距为2,过右焦点F的直线l与椭圆交于A,B两点,点M(2,0),设直线MA与直线MB的斜率分别为k1,k2.
(1)求椭圆方程;
(2)当直线l垂直x轴时,k1与k2有何关系?
(3)随着直线l的变化,k1+k2是否为定值?请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
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(1)求椭圆方程;
(2)当直线l垂直x轴时,k1与k2有何关系?
(3)随着直线l的变化,k1+k2是否为定值?请说明理由.
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