名校
解题方法
1 . 已知椭圆C:
的离心率为
,且
为C上一点.
(1)求C的标准方程;
(2)点A,B分别为C的左、右顶点,M,N为C上异于A,B的两点,直线MN不与坐标轴平行且不过坐标原点О,点M关于原点О的对称点为
,若直线
与直线BN相交于点P,直线OP与直线MN相交于点Q,证明:点Q位于定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f07da8a75cfce9b3a8b4eb202b820748.png)
(1)求C的标准方程;
(2)点A,B分别为C的左、右顶点,M,N为C上异于A,B的两点,直线MN不与坐标轴平行且不过坐标原点О,点M关于原点О的对称点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e10e10052bd862b0323ae961deacb353.png)
您最近一年使用:0次
2023-02-17更新
|
396次组卷
|
5卷引用:河南省十所名校2022-2023学年高三阶段性测试(四)文科数学试题
河南省十所名校2022-2023学年高三阶段性测试(四)文科数学试题河南省十所名校2022-2023学年高三阶段性测试(四)理科数学试题安徽省2022-2023学年高三下学期开学考数学试题河南省安阳市第一中学2022-2023学年高三阶段性测试(四)理科数学试题(已下线)专题3.9 圆锥曲线中的定点、定值、定直线问题大题专项训练【九大题型】-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)
2 . 已知椭圆C:
的上下顶点分别为
,过点P
且斜率为k(k<0)的直线与椭圆C自上而下交于
两点,直线
与
交于点
.
(1)设
的斜率分别为
,求
的值;
(2)求证:点
在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82766cfd2b7c59c7fac5b827ae5863b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ae6f48b9a53c0155a692509cf31f7e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc9055e1408371f84b8df59347ba7309.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f44755c5fee4b90266eac73ad47a128.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
(1)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6555f723dc0cfebda260dae93fd3f988.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c407500c3f3d395fdfdc366851ef3fac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
(2)求证:点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2022-08-26更新
|
1233次组卷
|
6卷引用:江苏省南京市六校联合体2022-2023学年高三上学期8月联合调研数学试题
江苏省南京市六校联合体2022-2023学年高三上学期8月联合调研数学试题(已下线)专题39 圆锥曲线中的定点、定值问题-2(已下线)第27讲 圆锥曲线中定直线问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)(已下线)专题24 圆锥曲线八类压轴题(解答题)-1(已下线)专题3.5 直线与椭圆的位置关系-重难点题型精讲-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)江苏省镇江中学2022-2023学年高三上学期12月月考数学试题
名校
解题方法
3 . 已知椭圆C:
=1
的左焦点为F,右顶点为A,离心率为
,M为椭圆C上一动点,
面积的最大值为
.
(1)求椭圆C的标准方程;
(2)过点M的直线l:y=kx+1与椭圆C的另一个交点为N,P为线段MN的中点,射线OP与椭圆交于点D.点Q为直线OP上一动点,且
,求证:点Q到x轴距离为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b475908640ed47eb77de085dce0cb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08894790c36962924b20d731a1ba069.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395b68bf47106a241e68e94e71a43232.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edb57d84f9bbcb3e30d4ce7e2e1e8604.png)
(1)求椭圆C的标准方程;
(2)过点M的直线l:y=kx+1与椭圆C的另一个交点为N,P为线段MN的中点,射线OP与椭圆交于点D.点Q为直线OP上一动点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a013a2aba586964ec6bc9cade0f460a.png)
您最近一年使用:0次
4 . 如图,A、B是椭圆
长轴的两个端点,M、N是椭圆上与A、B均不重合的相异两点,设直线AM、BN、AN的斜率分别是
、
、
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/04386e54-81a0-49fa-b703-62c580fa81a7.png?resizew=193)
(1)若直线MN过点
,求证:
为定值;
(2)设直线MN与x轴的交点为
(t为常数且
),试探究直线AM与直线BN的交点Q是否落在某条定直线上?若是,请求出该定直线的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.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/dbf434334b09cc0fdd4e86e84e6ceb00.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/7/04386e54-81a0-49fa-b703-62c580fa81a7.png?resizew=193)
(1)若直线MN过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8824f3fdb99f5768c6345039d556967.png)
(2)设直线MN与x轴的交点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fffad27b195220d9b31db743cd44eec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
您最近一年使用:0次
5 . 已知椭圆C:
的右焦点为F,上顶点为
,下顶点为
,
为等腰直角三角形,且直线
与圆
相切.
(1)求椭圆C的方程;
(2)过
的直线l交椭圆C于D,E两点(异于点
,
),直线
,
相交于点Q.证明:点Q在一条平行于x轴的直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.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/fae54b78e906f865fbdb351ffb4d335f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fee2afdacb11a6d025578bcaf576d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(1)求椭圆C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.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/7f1158eaa2e338f564eb18de5bef1d25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5e1bca493e452800f697c5c640b4aa3.png)
您最近一年使用:0次
2022-12-21更新
|
529次组卷
|
3卷引用:湖南省长沙市A佳教育联盟2022-2023学年高三上学期12月联考数学试题
湖南省长沙市A佳教育联盟2022-2023学年高三上学期12月联考数学试题湖南省株洲市部分学校2022-2023学年高三上学期12月联考数学试题(已下线)专题13 圆锥曲线压轴解答题常考套路归类(精讲精练)-1
6 . 已知动点P与定点
的距离和它到定直线
的距离之比为
,记P的轨迹为曲线C.
(1)求曲线C的方程;
(2)过点
的直线与曲线C交于
两点,
分别为曲线C与x轴的两个交点,直线
交于点N,求证:点N在定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495bb3e5a3a9d35f5c9f0cf1f5d51876.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求曲线C的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/363598fd39f2269952dc6ddd1201346c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e246a2eb095a4034be95fa8f09a56527.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/336fb966aa274635b0351ab1637cbc98.png)
您最近一年使用:0次
7 . 已知
为
的两个顶点,
为
的重心,边
上的两条中线长度之和为6.
(1)求点
的轨迹
的方程.
(2)已知点
,直线
与曲线
的另一个公共点为
,直线
与
交于点
,求证:当点
变化时,点
恒在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/395bbdcf87796c48d3a95fc923edb115.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.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/5881068127a39caf319492b4177204f0.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00127afdf543815af3ac4bc9bfc986a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f541f7ae7c39082d202efd28805c54e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/632917e61f4208959686d118c7f19231.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2022-07-05更新
|
928次组卷
|
6卷引用:三省三校2023届高三第一次联考文科数学试题
三省三校2023届高三第一次联考文科数学试题“三省三校”(南宁二中、南充中学、遵义四中)2023届高三第一次联考数学(理)试题河南省驻马店市新蔡县第一高级中学2021-2022学年高二下学期7月月考文科数学试题(已下线)专题39 圆锥曲线中的定点、定值问题-2新疆生产建设兵团第二师华山中学2023届高三上学期(提高、实验段)第三次月考数学(理)试题(已下线)专题3.16 圆锥曲线中的定点、定值、定直线问题大题专项训练(30道)-2022-2023学年高二数学举一反三系列(人教A版2019选择性必修第一册)
名校
解题方法
8 . 已知椭圆
:
的离心率为
,左、右顶点分别为
,
,上、下顶点分别为
,
,四边形
的面积为
.
(1)求椭圆
的方程;
(2)过点
且斜率存在的直线与椭圆相交于
,
两点,证明:直线
,
的交点
在一定直线上,并求出该直线方程.
![](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/8d5989c84e320b504511f23eeb6e7357.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/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92e5d91f4f631c580c155eba8c92bda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/453ea8f3a2b85526b54bf453871c3820.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bdfbae913ff7ff8caaefcaacf8c20ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79cc63cf907a27eeb15a06351348ec01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54fee2afdacb11a6d025578bcaf576d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
您最近一年使用:0次
2022-02-21更新
|
875次组卷
|
3卷引用:广东省揭阳华侨高级中学2022届高三上学期第二次阶段考试数学试题
广东省揭阳华侨高级中学2022届高三上学期第二次阶段考试数学试题广东省汕头市金山中学2022届高三下学期3月月考数学试题(B卷)(已下线)第27讲 圆锥曲线中定直线问题-【同步题型讲义】2022-2023学年高二数学同步教学题型讲义(人教A版2019选择性必修第一册)
2022高三·全国·专题练习
解题方法
9 . 已知椭圆
:
(
)的左右焦点分别为
,
,
分别为左右顶点,直线
:
与椭圆
交于
两点,当
时,
是椭圆的上顶点,且
的周长为
.
(1)求椭圆
的方程;
(2)设直线
交于点
,证明:点
在定直线上.
(3)设直线
的斜率分别为
,证明:
为定值.
![](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/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4231e4ff37aeb09d25d7cfd3f59cd7a.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/3949ed84c7cc1bcd74a3b17ec3b77ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2cfd997d3b66a3b8f7731b26f0ab0c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f8c4c029e552954bd493b49aeab82d5.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/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(3)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e4d7503a7d57ba242ad4e05c7006a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
10 . 已知椭圆
:
的离心率为
,长轴长为4.
(1)求椭圆
的方程;
(2)
为椭圆的左右顶点,
为椭圆的上顶点,设M是椭圆
上一点,且不与顶点重合,若直线
与直线
交于点
,直线
与直线
交于点
.求证:
为等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.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/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8dcc9f79fe5f07f25447aa442ee14ad.png)
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