名校
解题方法
1 . 已知椭圆
过点
,且椭圆
的离心率为
.
(1)求椭圆
的方程;
(2)若动点
在直线
上,过
作直线交椭圆
于
两点,且
为线段
的中点,再过
作直线
,证明:直线l恒过定点,并求出该定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a812a9b58ccba331cfd21d244329af01.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef00713e73b8357cc7900144f5505bc6.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e6ee852866de30427eb5fcd52cacbf8.png)
您最近一年使用:0次
2023-08-20更新
|
1821次组卷
|
9卷引用:天津市红桥区2024届高三一模数学试题
天津市红桥区2024届高三一模数学试题北京大学附属中学2022-2023学年高二下学期期中练习数学试题北京市第一○一中学2022-2023学年高二下学期期中练习数学试题江苏省“四校联盟”2023-2024学年高二上学期9月开学检测数学试题(已下线)3.1.2 椭圆的简单的几何性质(重难点突破)-【冲刺满分】2023-2024学年高二数学重难点突破+分层训练同步精讲练(人教A版2019选择性必修第一册)吉林省长春市农安县2023-2024学年高三上学期零模调研数学试题(已下线)考点17 解析几何中的定点与定直线问题 2024届高考数学考点总动员(已下线)第三章 圆锥曲线的方程(压轴必刷30题7种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)北京高二专题01平面解析几何
解题方法
2 . 已知椭圆
:
的离心率为
,左,右焦点分别为
,
,过点
的直线与椭圆相交于点
,
,且
的周长为8.
(1)求椭圆的标准方程;
(2)椭圆
的左,右顶点分别为
,
,上顶点为
,若过
且斜率为
的直线
与椭圆
在第一象限相交于点
,与直线
相交于点
,与
轴相交于点
,且满足
,求直线
的方程.
![](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)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8376a8a3dd42eaa0558501a3e2a2bdb4.png)
(1)求椭圆的标准方程;
(2)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10d8eb4a9f462ca0c1d49c3fe91e720d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7358dde6b9077405f34de8c22fda7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-05-21更新
|
1258次组卷
|
3卷引用:天津市滨海新区2023届高三三模数学试题
3 . 在平面直角坐标系
中,椭圆
的上,下焦点分别为
,椭圆上的任意一点到下焦点
的最大距离为3,最小距离为1.
(1)求椭圆
的方程;
(2)设过点
的直线
与椭圆
相交于点
,垂直于
的直线与
交于点
,与
轴交于点
,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7cd0b0bc751eea67c9519155b144f20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2d5e68bcbba909ed74f7f9205b7cb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a44b7b5fb0e2b975e99e30dcf9352b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
解题方法
4 . 已知椭圆
右焦点为
,已知椭圆短轴长为4,离心率为
.
(1)求椭圆的方程;
(2)若直线
与椭圆相交于M、N两点,线段MN垂直平分线与直线
及
轴和y轴相交于点D、E、G,直线GF与直线
相交于点
,记三角形EFG与三角形GDH的面积分别为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3c8bff78931350f73e15cc10995cc0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/235f0a6fb218d28383e6f27f2df1f50f.png)
您最近一年使用:0次
名校
解题方法
5 . 已知椭圆
过点
,且离心率为
.
(1)求椭圆C的方程;
(2)已知点
,点B在椭圆上(B异于椭圆的顶点),
为椭圆右焦点,点M满足
(O为坐标原点),直线AB与以M为圆心的圆相切于点P,且P为AB中点,求直线AB斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be112e60e2e0adcad51a2686ccdc42d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/830cb08b7ab0064d0092868153bb2d27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(1)求椭圆C的方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23e87d16c32b5aa4357f481b5808a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d89851284e50f4b7d11a3884a8ed9670.png)
您最近一年使用:0次
2023-04-05更新
|
833次组卷
|
3卷引用:天津市第四十七中学2022-2023学年高二下学期第一次阶段性检测数学试题
名校
解题方法
6 . 已知O为坐标原点,设椭圆
的离心率为
,过椭圆E上第一象限内一点P引x轴、y轴的平行线,分别交y轴、x轴于点A,B,且分别交直线
于点Q,R,记
与
的面积分别为
,
,满足
.
(1)求椭圆E的标准方程;
(2)已知点
,直线
交椭圆E于S,T两点,直线NS,NT分别与x轴交于C,D两点,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92febb64725497dd891a525e6f998e35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda3804b1fa07570002ac27483947fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/621f497734271f2bc2b4e86bf1dc6c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78a5d2f626f516fde9fe5647230828c6.png)
(1)求椭圆E的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77d269b408e9993d393f93947bb00063.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c311b215f3c3144fbe11ffacf386b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/015d0f4d316aaa8db15011340577b82d.png)
您最近一年使用:0次
2023-04-02更新
|
601次组卷
|
4卷引用:天津市南开大学附中2023-2024学年高二上学期第二次月考数学试题
天津市南开大学附中2023-2024学年高二上学期第二次月考数学试题河南省安阳市2023届高三第二次模拟考试文科数学试题(已下线)专题15圆锥曲线中的定点、定值、证明问题(已下线)专题15解析几何(解答题)
2023·天津红桥·一模
名校
解题方法
7 . 设椭圆
的左、右焦点分别为
,离心率
,长轴为4,且过椭圆右焦点
的直线
与椭圆
交于
两点.
(1)求椭圆C的标准方程;
(2)若
,其中
为坐标原点,求直线
的斜率;
(3)若
是椭圆
经过原点
的弦,且
,判断
是否为定值?若是定值,请求出,若不是定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2ebbb89a7c50ed23e32f1dcad606c30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7605ce6f221ce8cad191da0f84a216d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4487b728410d4ddbfedc150990109dba.png)
您最近一年使用:0次
2023-03-29更新
|
1487次组卷
|
5卷引用:天津市红桥区2023届高三一模数学试题
(已下线)天津市红桥区2023届高三一模数学试题天津市红桥区2023届高三一模考试数学试题云南省凤庆县第一中学2022-2023学年高二下学期期中考试数学试题(已下线)重难点突破06 弦长问题及长度和、差、商、积问题(七大题型)-2宁夏吴忠市2024届高三下学期高考模拟联考(一)文科数学试题
解题方法
8 . 在平面直角坐标系
中,椭圆
的离心率为
,点
是椭圆与
轴负半轴的交点,点
是椭圆与
轴正半轴的交点,且直线
与圆
相切.
(1)求椭圆
的方程;
(2)已知斜率大于0的直线
与椭圆
有唯一的公共点
,过点
作直线
的平行线交椭圆
于点
,若
的面积为
,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/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7660b07cf2fe7e8d7ac4992969299916.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知斜率大于0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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c0da03ec477a5e17b7f4de370638024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.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
9 . 已知椭圆
上任意一点到两个焦点
,
的距离的和为4.经过点
且不经过点
的直线与椭圆C交于P,Q两点,直线
与直线
交于点E,直线
与直线
交于点N.
(1)求椭圆C的标准方程;
(2)求证:
的面积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4a7482cb81b34df5a11807b8136a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60cfc83cab6cd17842f28b9c37836673.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ee8669bc280bff4b20644cb82faf23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48d25e70d37af93796965efc8d342185.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5adb5eb60ae4435a12d93854066298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be2e2c0d4ac2bd79f6cea7a9b1a50662.png)
(1)求椭圆C的标准方程;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c48e42ce4fd7e6da946bf2b7b22200db.png)
您最近一年使用:0次
2023-02-22更新
|
705次组卷
|
2卷引用:天津市南开区2022-2023学年高二上学期1月阶段性质量监测数学试题
名校
解题方法
10 . 已知椭圆
的左,右顶点分别为
,上顶点M与左,右顶点连线
的斜率乘积为
,焦距为
.
(1)求椭圆
的方程;
(2)设过点
的直线
与椭圆C交于
两点,O为坐标原点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1c6ba69264c8f203cd756581bc6280a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/319ff9f648fedec284a11a9761cb6183.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-17更新
|
279次组卷
|
2卷引用:天津市瑞景中学2023-2024学年高二上学期期中考试数学试卷