名校
解题方法
1 . 已知椭圆
的长轴长为4,上顶点为
,左、右焦点分别为
,
,且
,
为坐标原点.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设点
,
为椭圆
上的两个动点,
,问:点
到直线
的距离
是否为定值?若是,求出
的值;若不是.请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/74064c3fa84f604f6636f6bbf778bdc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2020-10-25更新
|
948次组卷
|
9卷引用:河南省商丘市第一高级中学2020-2021学年高二下学期3月月考数学理科试题
名校
解题方法
2 . 已知椭圆
:
(
)过点
,离心率
,直线
:
与椭圆
交于
,
两点.
(1)求椭圆
的方程;
(2)是否存在定点
,使得
为定值.若存在,求出点
的坐标和
的值;若不存在,请说明理由.
![](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/d8da36e3081bfe5d32c9ec70be4da3da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6767830cc1811f0f4ea5a008fdc7e723.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)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)是否存在定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12cb3517a4990da3f81dacc605c77768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12cb3517a4990da3f81dacc605c77768.png)
您最近一年使用:0次
2020-08-06更新
|
356次组卷
|
2卷引用:河南省顶尖名校2020-2021学年高二下学期5月联考理科数学试卷
名校
解题方法
3 . 已知椭圆
:
的离心率为
,左、右焦点分别为
,
,且
到直线
:
的距离为
.
(1)求椭圆
的标准方程;
(2)若直线
:
与椭圆
交于
,
两个不同的点,
为坐标原点,
是椭圆
上的一点,且四边形
是平行四边形,求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d1faa06cb0c5de12350da3768454f4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae96f5020aef5aef03ec7f406460f608.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/1dde8112e8eb968fd042418dd632759e.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/134661dcfb2a8f82f30f439090e8261a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134661dcfb2a8f82f30f439090e8261a.png)
您最近一年使用:0次
2020-07-31更新
|
1037次组卷
|
6卷引用:河南省许昌实验中学2020-2021学年高二下学期期末数学(文科)试题
名校
解题方法
4 . 已知点
为坐标原点,椭圆
:
的右焦点为
,
为椭圆
上一点,椭圆
上异于
的两点
,
满足
,当
垂直于
轴时,
.
(1)求椭圆
的标准方程;
(2)设直线
,
分别与
轴交于点
,
,问:
的值是否为定值?若是,请求出
的值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](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/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62868b606ed0e29a4712bf75f335b5dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fb26d84907c923278ac4626a9d58947.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6196f68aa254e0bc1061551d47bb934c.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b62769b7177ef4bc952dc1dd51d6b510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883f23ab75b490d6e9e03b8ff8b269c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1019d4ad2e3fb4a7abb66e0e9e55b556.png)
您最近一年使用:0次
2020-05-31更新
|
495次组卷
|
6卷引用:河南省豫西名校联盟2020-2021学年高二上学期测试(一)文科数学试题
名校
解题方法
5 . 已知椭圆
的离心率为
,以椭圆
的长轴和短轴为对角线的四边形的面积为
.
(1)求椭圆
的方程;
(2)若直线
与椭圆
相交于
,
两点,设
为椭圆
上一动点,且满足
(
为坐标原点).当
时,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67e4b79aaab10cccde470d408ec9f0f5.png)
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4dfccfba0f6b1c0762a9cb37c3f6fff0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18419ab2d7cde42b1130e9894dc5b9e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2020-03-24更新
|
312次组卷
|
2卷引用:河南省杞县高中2021-2022学年高三上学期第四次月考理科数学试题
名校
解题方法
6 . 已知椭圆C:
(
)的左右焦点分别为
,如果C上存在一点Q,使
,则椭圆的离心率
的取值范围为
![](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/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a45960e50d860715b8ed4afe8c932997.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-02-12更新
|
2708次组卷
|
8卷引用:河南省漯河市高级中学2021-2022学年高二上学期期中数学试题
河南省漯河市高级中学2021-2022学年高二上学期期中数学试题重庆市第八中学2021-2022学年高二上学期半期数学试题四川省绵阳市江油中学2021-2022学年高二上学期10月月考数学(理)试题河北省保定市顺平县中学2021-2022学年高二上学期第三次月考数学试题河北省唐山市第十一中学2021-2022学年高二上学期12月月考数学试题(已下线)期末重难点突破专题02-【尖子生专用】2021-2022学年高二数学考点培优训练(人教A版2019选择性必修第一册)天津市和平区耀华中学2019-2020学年高二上学期期末数学试题人教A版(2019) 选择性必修第一册 过关斩将 第三章 圆锥曲线的方程 3.1 综合拔高练
名校
7 . 已知椭圆
的左、右焦点分别为
,
,离心率为
,过
作直线
与椭圆
交于
,
两点,
的周长为8.
(1)求椭圆
的标准方程;
(2)问:
的内切圆面积是否有最大值?若有,试求出最大值;若没有,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/f5076289823db419f94e9c0c8f4aafd9.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)问:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
您最近一年使用:0次
2020-01-13更新
|
1017次组卷
|
12卷引用:河南省三门峡市2020-2021学年度高三第一次大练习数学(理科)试题
(已下线)河南省三门峡市2020-2021学年度高三第一次大练习数学(理科)试题(已下线)必刷卷01-2021年高考数学考前信息必刷卷(江苏专用)(已下线)必刷卷04-2021年高考数学考前信息必刷卷(山东专用)(已下线)必刷卷08-2021年高考数学考前信息必刷卷(江苏专用)福建省宁德市2019-2020学年高三上学期第一次质量检查(期末)数学理试题山东师范大学附属中学2019-2020学年高三4月线上模拟数学试题2020届山东省平邑县第一中学高三下学期第五次调研考试数学试题(已下线)文科数学-6月大数据精选模拟卷02(新课标Ⅲ卷)(满分冲刺篇)(已下线)理科数学-6月大数据精选模拟卷02(新课标Ⅲ卷)(满分冲刺篇)山东省潍坊高密市2020届高三模拟数学试题一河北省石家庄市辛集市第一中学2021届高三上学期九月月考数学试题湖南省常德市第一中学2020-2021学年高三上学期第四次月考数学试题
8 . 在直角坐标系xOy中,动点P与定点
的距离和它到定直线
的距离之比是
,设动点P的轨迹为E.
(1)求动点P的轨迹E的方程;
(2)设过F的直线交轨迹E的弦为AB,过原点的直线交轨迹E的弦为CD,若
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求动点P的轨迹E的方程;
(2)设过F的直线交轨迹E的弦为AB,过原点的直线交轨迹E的弦为CD,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1791846aaa3ff3c22c9d751a6500275.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f14b014b0be63514079243a914c7d20e.png)
您最近一年使用:0次
2019-11-14更新
|
1141次组卷
|
5卷引用:河南省鹤壁市高级中学2020-2021学年高三上学期第一次模拟测试(8月段考)数学(理)试题
名校
9 . 已知椭圆
的右焦点为
,且离心率为
,
的三个顶点都在椭圆
上,设
三条边
的中点分别为
,且三条边所在直线的斜率分别为
,且
均不为0.
为坐标原点,若直线
的斜率之和为1.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dddcb841e17cc8df9c1aa78bc1b12c1.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45054144b49c1bcc5dc116e024eaec03.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
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2018-03-29更新
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2107次组卷
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6卷引用:河南省洛阳复兴学校2021-2022学年高二上学期12月月考数学试题
河南省洛阳复兴学校2021-2022学年高二上学期12月月考数学试题河南省郑州市2018年高中毕业年级第二次质量预测---文科数学河南省郑州市2018届高三毕业年级第二次质量预测理科数学试题河南省焦作市博爱英才学校2020-2021学年高二第一学期11月月考文科数学试题安徽省阜阳第一中学2019-2020学年高二上学期期中数学(理)试题(已下线)专题9-1 圆锥小题压轴九类-2022年高考数学毕业班二轮热点题型归纳与变式演练(全国通用)
解题方法
10 . 已知椭圆
的右焦点为
,上顶点为
,直线
与直线
垂直,椭圆
经过点
.
(1)求椭圆
的标准方程;
(2)过点
作椭圆
的两条互相垂直的弦
.若弦
的中点分别为
,证明:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c63e36329f5e0979f5ee776ac5d06327.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b386e2c5d9ad7cec404ce5c40dbebe42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480f004c98a0df86a35a48bc973f0472.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5c4cd264c97c1f261229925cc5a6761.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2018-01-18更新
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918次组卷
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2卷引用:河南省新乡市第十一中学2020-2021学年高二下学期第二次月考文科数学试题