名校
解题方法
1 . 已知
、
,若动点
满足
.
(1)求动点
的轨迹
的方程;
(2)若斜率为1的直线
与曲线
交于
,
两点,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65368687df4d7e3b9304e85ec4de354c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d94eced0532ab12eccb9318e491e39c.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若斜率为1的直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/131ddf8348068267ed80a2e915fe8503.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
解题方法
2 . 已知结论:椭圆
上一点
处切线方程为
.试用此结论解答下列问题.如图,已知椭圆
:
的右焦点为
,原点为
,椭圆的动弦AB过焦点
且不垂直于坐标轴,弦
的中点为
,椭圆
在点A,B处的两切线的交点为
.
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a271c22e34d4df61636ab3052a8e0ecc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1185a977aa9dc61d23db4b658126f8a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/baa77802f9a072a800ee5098f668d5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/3/19/b9703fbb-7e2a-404b-bdfe-c1c16369ef43.png?resizew=161)
(1)试判断:O,M,N三点是否共线若三点共线,请给出证明;若三点不共线,请说明理由;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfba099195b252ab0faba0d8360fae98.png)
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解题方法
3 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆
的标准方程;
(2)设椭圆
的左顶点为
,上顶点为
,已知直线
平行于直线
,且交椭圆
于
两点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63bb539d82e21ff9052cccaa62ef849.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/736a205640aaabdd8caace743963d4a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
4 . 已知椭圆
:
.
(1)直线
:
交椭圆
于
,
两点,求线段
的长;
(2)
为椭圆
的左顶点,记直线
,
,
的斜率分别为
,
,
,若
,试问直线
是否过定点,若是,求出定点坐标,若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/271e595c257e4c0ade90a9bbbf0e6b0d.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fcfd2fe527d76490e694de333166ecb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
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2023-09-29更新
|
2097次组卷
|
5卷引用:浙江省名校协作体2022-2023学年高二下学期联考数学试题
浙江省名校协作体2022-2023学年高二下学期联考数学试题(已下线)模块四 专题6 大题分类练(圆锥曲线的方程)拔高能力练(人教A)(已下线)第3章 圆锥曲线与方程章末题型归纳总结-【帮课堂】2023-2024学年高二数学同步学与练(苏教版2019选择性必修第一册)(已下线)专题3.1 椭圆(5个考点十四大题型)(5)四川省南充市嘉陵第一中学2023-2024学年高二下学期4月期中考试数学试题
5 . 如图,已知直线
和椭圆
.m为何值时,直线l与椭圆C:
(1)有两个公共点?
(2)有且只有一个公共点?
(3)没有公共点?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0916564f10f6cecbcf9e5b8ef1bd6a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee9ce51f55008258322bbe19810f62d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/9/21/3d51a9c9-c5bc-45d5-8549-00c2c6a1175c.png?resizew=185)
(1)有两个公共点?
(2)有且只有一个公共点?
(3)没有公共点?
您最近一年使用:0次
2023-09-19更新
|
858次组卷
|
7卷引用:人教A版(2019)选择性必修第一册课本例题3.1 椭圆
人教A版(2019)选择性必修第一册课本例题3.1 椭圆(已下线)3.1.2椭圆的标准方程及性质的应用(第2课时)(导学案)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)(已下线)考点巩固卷20 椭圆方程及其性质(十大考点)宁夏银川市第六中学2023-2024学年高二上学期期中考试数学试题(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)专题23 椭圆的简单几何性质10种常见考法归类(2)(已下线)专题10 椭圆的几何性质8种常见考法归类(2)
23-24高二上·全国·课后作业
名校
6 . 已知直线
,椭圆
.试问当m取何值时,直线l与椭圆C:
(1)相交;
(2)相切;
(3)相离?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7eff5ecd1b7c0009d2ebaed7d9fb6fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
(1)相交;
(2)相切;
(3)相离?
您最近一年使用:0次
2023-09-11更新
|
308次组卷
|
6卷引用:3.1 椭圆
(已下线)3.1 椭圆(已下线)2.4.2直线与圆锥曲线的综合问题(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)湘教版(2019)选择性必修第一册课本习题 习题3.1广东省湛江市第二十中学2023-2024学年高二上学期11月期中数学试题(已下线)第04讲 拓展一:直线与椭圆的位置关系-【练透核心考点】2023-2024学年高二数学上学期重点题型方法与技巧(人教A版2019选择性必修第一册)(已下线)专题05 椭圆及其性质(3大考点9种题型)(考点清单)-2023-2024学年高二数学上学期期中考点大串讲(苏教版2019选择性必修第一册)
解题方法
7 . 已知椭圆
的右顶点为
,上顶点为
,左、右焦点分别为
为原点,且
,过点
作斜率为
的直线
与椭圆
交于另一点
,交
轴于点
.
(1)求椭圆
的方程;
(2)设
为
的中点,在
轴上是否存在定点
,对于任意的
都有
?若存在,求出定点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/448c0a5ee776d19ce8e42ac9a5fd27c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7dd2722e9cb4052fedd9b78dcf014b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b68d521e5a49f4e9d9d9e59cbf407280.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bbb3f7e8ea021b4adb7f430daa7fadd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2799abb64fd7bfce9dfa7228aa460564.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0297c11050f2e39f82bb2cdf810d4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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2023-08-07更新
|
1365次组卷
|
5卷引用:陕西省西安市阎良区2020-2021学年高二上学期期末理科数学试题
陕西省西安市阎良区2020-2021学年高二上学期期末理科数学试题陕西省渭南市华阴市2020-2021学年高二上学期期末理科数学试题陕西省延安市宝塔区第四中学2020-2021学年高二上学期期末理科数学试题(已下线)第三章 圆锥曲线的方程 章末测试(提升)-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)江西省上饶市广丰区南山中学2023-2024学年高二上学期期末模拟数学试题
解题方法
8 . 已知两动直线
,
分别过椭圆
的左焦点和中心,当
过椭圆上顶点时,直线
的距离为
.
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953847934976000/2954472989630464/STEM/3969b115-4e72-47b5-b725-7a1e10447bd1.png?resizew=251)
(1)求椭圆C的方程;
(2)设
与椭圆C交于A,B两点,点A关于
的对称点为
,若经过点A,
,B的圆的圆心为点M,求点M横坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56434d9b23622192a4da9850096470d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93408b6d58339be6d3cc16cdd64c58f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/2022/4/8/2953847934976000/2954472989630464/STEM/3969b115-4e72-47b5-b725-7a1e10447bd1.png?resizew=251)
(1)求椭圆C的方程;
(2)设
![](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/e7c314398e26ffc7164b82946eeb4273.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c314398e26ffc7164b82946eeb4273.png)
您最近一年使用:0次
名校
解题方法
9 . 已知椭圆
的左、右焦点分别为
,
,点
满足
,且
的面积为
.
(1)求椭圆C的方程;
(2)设E、F是椭圆C上的两个动点,O为坐标原点,直线OE的斜率为
,直线OF的斜率为
,求当
为何值时,直线EF与以原点为圆心的定圆相切,并写出此定圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.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/fa1da31f31ed82b89a62e2a8b7c1ce45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb1b3fdaa48126d0dd7eeeb13d563ead.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42fc33bcfc63ec2f4940ccd3f862400.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C的方程;
(2)设E、F是椭圆C上的两个动点,O为坐标原点,直线OE的斜率为
![](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/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2022-03-05更新
|
592次组卷
|
4卷引用:安徽省皖南地区2021-2022学年高二下学期开学调研考试数学试题
安徽省皖南地区2021-2022学年高二下学期开学调研考试数学试题内蒙古赤峰红旗中学2021-2022学年下学期高二年级期中考试数学试题山西大学附属中学校2022-2023学年高二上学期12月月考数学试题(已下线)第3章 圆锥曲线的方程(基础、典型、易错、新文化、压轴)(1)
21-22高二·全国·课后作业
10 . 已知直线
和椭圆
.分别求直线l与椭圆C有两个公共点、只有一个公共点和没有公共点时k的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94a8d6991873e79b298984a95b8954b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9bf37fb661ccc2fdd67407269708df4.png)
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