名校
解题方法
1 . 已知椭圆
的离心率为
,短轴长为2,过点
斜率不为0的直线
与椭圆有两个不同的交点A,B.
(1)求椭圆的标准方程;
(2)椭圆左右顶点为M,N,设
中点为Q,直线
交直线
于点R,
是否为定值,若是请求出定值,若不是请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cf6cca367ce2afd96d7d951f9587e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求椭圆的标准方程;
(2)椭圆左右顶点为M,N,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/073ee2d24f266cb56a4579d45093ed7e.png)
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆
过点
.其左、右两个焦点分别为
、
,短轴的一个端点为B,且
.
(1)求椭圆的标准方程:
(2)设直线
:
与椭圆交于不同的两点M,N,且O为坐标原点,若
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5891f86f0a02a830d3247f16516f18c7.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/af1df54d9a0dc61187f219d4d27217ad.png)
(1)求椭圆的标准方程:
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f253946dde5a3af7ccf4eb0cab4c8e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-11-23更新
|
344次组卷
|
2卷引用:江西省南昌市第二中学2023-2024学年高二上学期期中考试数学试卷
名校
解题方法
3 . 已知椭圆
的左、右焦点为
,
,离心率为
.点P是椭圆C上不同于顶点的任意一点,射线
、
分别与椭圆C交于点A、B,
的周长为8.
(1)求椭圆C的标准方程;
(2)若
,
,求证:
为定值.
![](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/f89eef3148f2d4d09379767b4af69132.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/8144da365530cc0560de2d4946c96a1d.png)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/678764669f89f7f7c1e2f986b642b466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5749effb19c4a35500b1b1162e33c24.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
您最近一年使用:0次
2023-09-30更新
|
2618次组卷
|
12卷引用:江西省南昌市第十九中学2024届高三上学期11月期中考试数学试题
江西省南昌市第十九中学2024届高三上学期11月期中考试数学试题四川省南充高级中学2022-2023学年高三下学期第三次模拟数学文科试题内蒙古赤峰二中2023-2024学年高三上学期第二次月考理科数学试题(已下线)单元提升卷10 平面解析几何(已下线)阶段性检测4.1(易)(范围:高考全部内容)(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)考点16 解析几何中的定值问题 2024届高考数学考点总动员【练】安徽省安庆市桐城市桐城中学2023-2024学年高二上学期第二次教学质量检测数学试题(已下线)专题3-2 椭圆大题综合11种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)(已下线)第八章 解析几何综合测试B(提升卷)(已下线)专题23 椭圆的简单几何性质10种常见考法归类(3)(已下线)专题10 椭圆的几何性质8种常见考法归类(2)
4 . 已知椭圆
的一个焦点为
,且过点
.
(1)求椭圆
的方程;
(2)直线
与椭圆
交于
两点,求
面积的最大值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be92f0e0012a7696c78e3e00513edefd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6f11c964b3a008d35fb4b3ac18ed5a5.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc68ef6b89afc972832cfca71a5b120.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/25dd698d57d1cf239eb8752aecaaa4f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-08-27更新
|
481次组卷
|
3卷引用:江西省南昌市外国语学校2024届高三上学期8月月考(第一次保送考试)数学试题
江西省南昌市外国语学校2024届高三上学期8月月考(第一次保送考试)数学试题(已下线)人教A版2019选择性必修第一册综合测试(基础)-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)江苏省连云港市灌南高级中学2023-2024学年高三上学期第一次月考数学试题
名校
解题方法
5 . 已知椭圆
:
,过左焦点
作倾斜角为
的直线
交椭圆
于
两点.当直线
的倾斜角为
时
.
(1)求椭圆
的标准方程;
(2)点
为坐标原点,求
面积的最大值;并求此时直线
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/46542271c7fa06f33b222424838c9684.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/037fb348109dc2063a268b10eb925a57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbf87ae3ce995c99c57b7226cdb7598e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
解题方法
6 . 已知椭圆
的左、右焦点分别为
点
在
上,
的周长为
,面积为
.
(1)求
的方程.
(2)设
的左、右顶点分别为
,过点
的直线
与
交于
两点(不同于左右顶点),记直线
的斜率为
,直线
的斜率为
,则是否存在实常数
,使得
恒成立.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65abb60103949a9cbe1e4890df8bd3ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23186d30e2939a79c5f9cd71b61f4bcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3643fa70165ed9fef1398bc9443e7a02.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1a10220fb06a9f6dfb2d2e84d1a4504.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3162fc8aced6ab452d3007f914c2f6ab.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/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34bc0ee0a95fab04edf648026f14b9ff.png)
您最近一年使用:0次
2023-08-18更新
|
718次组卷
|
4卷引用:江西省南昌市东湖区南昌市八一中学2023届高三上学期2月月考文科数学试题
江西省南昌市东湖区南昌市八一中学2023届高三上学期2月月考文科数学试题河北省石家庄市第二中学2023届高三下学期2月月考数学试题(已下线)重难点突破09 一类与斜率和、差、商、积问题的探究(四大题型)(已下线)专题3-2 椭圆大题综合11种题型归类(讲+练)-【巅峰课堂】2023-2024学年高二数学热点题型归纳与培优练(人教A版2019选择性必修第一册)
名校
解题方法
7 . 已知离心率为
的椭圆C:
过点
,椭圆上有四个动点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f26dfcdde7fc4ba496c481fcca3324c.png)
,
与
交于
点.如图所示.
(1)求曲线C的方程;
(2)当
恰好分别为椭圆的上顶点和右顶点时,试探究:直线
与
的斜率之积是否为定值?若为定值,请求出该定值;否则,请说明理由;
(3)若点
的坐标为
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2663eb82722aa0ec9355f1c4680e42d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f26dfcdde7fc4ba496c481fcca3324c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3402ea855e2ae2dcd98f607bef4fdd6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/7/26/12436883-162c-4552-b396-736234f35646.png?resizew=215)
(1)求曲线C的方程;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba31c1dd27defc2621e4fb4d7006f7f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
名校
解题方法
8 . 已知
的两顶点坐标
.
(1)求动点
的轨迹
的方程;
(2)不垂直于
轴的动直线
与轨迹
相交于
两点,定点
,若直线
关于
轴对称,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6ba809e0492f485fdaee0478e2c588.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)不垂直于
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af74113f38fffeed8075e57d7f9d2533.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/378f90fe1e622bab7a8fb2ccdc0c11cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
您最近一年使用:0次
2023-06-20更新
|
366次组卷
|
5卷引用:江西省南昌市铁路第一中学2023-2024学年高二上学期12月月考数学试卷
江西省南昌市铁路第一中学2023-2024学年高二上学期12月月考数学试卷江西省赣州市六校联盟2022-2023学年高二下学期5月联合测评数学试题(已下线)第10讲 拓展四:圆锥曲线的方程(面积问题)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)第01讲 3.1.1椭圆及其标准方程(3)(已下线)河北省石家庄市河北省实验中学2024届高三上学期名校联考数学试题变式题19-22
解题方法
9 . 已知椭圆
的焦距为
,左、右顶点分别为
,上顶点为B,且
.
(1)求椭圆C的方程;
(2)若过
且斜率为k的直线l与椭圆C在第一象限相交于点Q,与直线
相交于点P,与y轴相交于点M,且
.求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1735708848cfde06947647a29687a76.png)
(1)求椭圆C的方程;
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f69a7effc74ab83bd02bb4c2d9e9716.png)
您最近一年使用:0次
2023-04-23更新
|
306次组卷
|
3卷引用:江西省南昌市2023届高三二模数学(文)试题
解题方法
10 . 已知椭圆
的焦距为
,左、右顶点分别为
,上顶点为B,过点
的直线
斜率分别为
,直线
与直线
的交点分别为B,P.
(1)求椭圆C的方程;
(2)若直线
与椭圆C的另一个交点为Q,直线
与x轴的交点为R,记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77b5b9d91f873a3e72ebad138fdb109b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
(1)求椭圆C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb6ede9761b5b90f8dc137708e1ee90f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9231930ca3d540a69694cbdf9ebe28.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
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