名校
解题方法
1 . 已知椭圆
:
(
)的左、右焦点分别为
,
,离心率为
,点
是椭圆上一点,
的周长为
.
(1)求椭圆
的方程;
(2)直线
:
与椭圆
交于
,
两点,且四边形
为平行四边形,求证:
的面积为定值.
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5eb4f6a7cd67eb76bc9f8b353c4059d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ac988c3805bb84dd0a10fde30be2538.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.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/9d897c89e28895e87b2eeab741351525.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d897c89e28895e87b2eeab741351525.png)
您最近一年使用:0次
2021-03-28更新
|
2282次组卷
|
5卷引用:安徽省六安市舒城中学2021届高三下学期仿真模拟(二)文科数学试题
名校
2 . 已知椭圆
,过椭圆左焦点F的直线
与椭圆C在第一象限交于点M,三角形MFO的面积为
.
(1)求椭圆C的标准方程;
(2)过点M作直线l垂直于x轴,直线MA、MB交椭圆分别于A、B两点,且两直线关于直线l对称,求证∶直线AB的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0717cf6826af5a27b5956f3b2943168f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802e162b98c280720fcb909cf392fda3.png)
(1)求椭圆C的标准方程;
(2)过点M作直线l垂直于x轴,直线MA、MB交椭圆分别于A、B两点,且两直线关于直线l对称,求证∶直线AB的斜率为定值.
您最近一年使用:0次
2021-02-28更新
|
1317次组卷
|
3卷引用:安徽省安庆市2021届高三下学期一模理科数学试题
3 . 在平面直角坐标系
中,点
为动点,已知点
,
,直线
与
的斜率之积为定值
.
(1)求动点
的轨迹
的方程;
(2)若
,过点
的直线
交轨迹
于
、
两点,以
为对角线的正方形的第三个顶点恰在
轴上,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0338630beeca9e7fa803f63f6b1ce089.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fcb73920188f0215bd21a0148eeebed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-08-04更新
|
1310次组卷
|
2卷引用:安徽省滁州市民办高中2019-2020学年高二下学期期末数学(文)试题
名校
解题方法
4 . 已知椭圆
经过点
,且离心率为
,过其右焦点F的直线
交椭圆C于M,N两点,交y轴于E点.若
,
.
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)试判断
是否是定值.若是定值,求出该定值;若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b0dadb875cccce870b69409a476606.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e90064d012356de1877aa697cd6d6ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e834d81e4c7a5eeda2ee6a2f961b2af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1d78bf57b49e6c5c4783ee78738efad.png)
(Ⅰ)求椭圆C的标准方程;
(Ⅱ)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32705e629d8b9187b53efeee6605af15.png)
您最近一年使用:0次
2020-05-15更新
|
584次组卷
|
5卷引用:2020届安徽省示范高中皖北协作区高三下学期第22届联考文科数学试题
2020届安徽省示范高中皖北协作区高三下学期第22届联考文科数学试题四川省宜宾市叙州区第一中学校2019-2020学年高二下学期期末模拟考试数学(文)试题四川省宜宾市叙州区第一中学校2019-2020学年高二下学期期末模拟考试数学(理)试题(已下线)文科数学-2021年高考押题预测卷(新课标Ⅰ卷)01(已下线)江西省九所重点中学2023届高三第二次联考联合考试数学(文)试题变式题16-20
名校
5 . 直角坐标系
中,椭圆
的离心率为
,过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆
的方程;
(2)已知点
,斜率为
的直线
与椭圆
相交于
两点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ef233ad3db01fa3ce9ee94eaad8e64e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289542670b804bc81f924549035232f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-03-26更新
|
549次组卷
|
4卷引用:2020届安徽省阜阳市临泉二中高三第五次教学质量检测数学(理)试题
2020届安徽省阜阳市临泉二中高三第五次教学质量检测数学(理)试题安徽省六安市舒城中学2021-2022学年高二下学期第二次月考数学试题(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(已下线)专题1 解析几何与平面向量
名校
解题方法
6 . 已知椭圆
的左、右焦点分别为
,上、下顶点分别为
,若
,点
关于直线
的对称点在椭圆
上.
(1)求椭圆
的方程与离心率;
(2)过点
作直线
与椭圆
相交于两个不同的点
;若
恒成立,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b147b2c5af1650605d4bd2a94a506b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1248fb34b191f243c6dd506775a5be11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa482d7bcaa385bfc3548b42a4bfb60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d594ca430a791b79a969c2f83aa230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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名校
7 . 设椭圆
的长轴长
,离心率为
,定义直线
为椭圆的类准线,若椭圆C的类准线方程为
,
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/0c0b5bba-283d-4b0a-b5dc-195b9d84e9a2.png?resizew=162)
(1)求椭圆C的方程;
(2)如图,不垂直于x轴的直线
与椭圆C交于A、B两点,点
在直线l的左上方,且
,直线PA、PB分别与y轴交于点M、N,若线段MN长度是4,求k.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3337ce20986618e4c9ba74063c5aa3d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a7e850fd3db1a8ae7082557fb344de0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/22/0c0b5bba-283d-4b0a-b5dc-195b9d84e9a2.png?resizew=162)
(1)求椭圆C的方程;
(2)如图,不垂直于x轴的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b32838e41c93a5aa10d2ce2d023d8b87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83640592853a53872d7af69c0cffc1bb.png)
您最近一年使用:0次
名校
解题方法
8 . 已知A是圆O:x2+y2=4上一动点,过点A作AB⊥x轴,垂足为B,动点D满足
.
(1)求动点D的轨迹C的方程;
(2)垂直于x轴的直线M交轨迹C于M、N两点,点P(3,0),直线PM与轨迹C的另一个交点为Q.问:直线NQ是否过一定点?若过定点,求出该定点的坐标;若不过定点,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7a1a254226053cfd7f8cafd6440e8a1.png)
(1)求动点D的轨迹C的方程;
(2)垂直于x轴的直线M交轨迹C于M、N两点,点P(3,0),直线PM与轨迹C的另一个交点为Q.问:直线NQ是否过一定点?若过定点,求出该定点的坐标;若不过定点,请说明理由.
您最近一年使用:0次
解题方法
9 . 如图,已知椭圆E的右焦点为
,P.Q为椭圆上的两个动点,
周长的最大值为8.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/ad0f9634-0ccf-4848-8d50-d0308e7d026b.png?resizew=201)
(1)求椭圆E的标准方程;
(2)记椭圆E的左焦点为
,过
作直线l与椭圆交于不同两点M.N,求
面积取最大值时的直线l方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fea5f7430235e65d2c2e6b2ecc46712.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/22/ad0f9634-0ccf-4848-8d50-d0308e7d026b.png?resizew=201)
(1)求椭圆E的标准方程;
(2)记椭圆E的左焦点为
![](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/76ea1c3fe8431260ecb8dffcdae8d570.png)
您最近一年使用:0次
名校
10 . 已知椭圆
的长轴长为
,且短轴长是长轴长的一半.
(1)求椭圆的方程;
(2)经过点
作直线
,交椭圆于
、
两点.如果
恰好是线段
的中点,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求椭圆的方程;
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97caea8ea20c118920d887d2ee9ac83d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2019-12-01更新
|
1130次组卷
|
5卷引用:安徽省阜阳市第三中学2019-2020学年高二上学期10月月考数学(文)试题