名校
解题方法
1 . 设椭圆
:
的左顶点为A,左焦点为
.已知椭圆的离心率为
,过点A的直线
与椭圆交于另一点
,且点
与点
关于
轴对称(
与
不重合).若直线
与直线
垂直,垂足为
,且
的面积
.
(1)求直线
的斜率;
(2)求椭圆
的方程.
![](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/a0ed1ec316bc54c37c4286c208f55667.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/7f9e8449aad35c5d840a3395ea86df6d.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/81dea63b8ce3e51adf66cf7b9982a248.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/4cae70b8a9d2d2e96dea62c00ced04b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f25d95565e1e7f522624ed32e5a61199.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6902f0bd1e881596b70b5d7dac9bda46.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
您最近一年使用:0次
2023-11-11更新
|
507次组卷
|
2卷引用:天津市和平区天津一中2024届高三上学期第三次月考数学试题
名校
解题方法
2 . 记![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f95748e120a8048a0a01c8182ec15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5850594a09755770a8225da182bd52.png)
,若
有三个不等实根
,若
,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d17f95748e120a8048a0a01c8182ec15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc5850594a09755770a8225da182bd52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef2ca0936339711b0173fc4620623621.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf6902c9f2a26385b1daadd855fc1436.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1310a7a80d1f8751a3f8cafe7f8c8b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f1037287a6d8a9a7766734077faa87b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/380bbacf854e30e2e747fc286d2b9997.png)
您最近一年使用:0次
2022-11-23更新
|
528次组卷
|
2卷引用:天津市耀华中学2022-2023学年高三上学期第二次月考数学试题
名校
解题方法
3 . 定义椭圆
的“蒙日圆”的方程为
,已知椭圆
的长轴长为4,离心率为
.
(1)求椭圆
的标准方程和它的“蒙日圆”E的方程;
(2)过“蒙日圆”E上的任意一点M作椭圆
的一条切线
,A为切点,延长MA与“蒙日圆”E交于点
,O为坐标原点,若直线OM,OD的斜率存在,且分别设为
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ee9d4ad39e56940f519bd3acc5e85ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过“蒙日圆”E上的任意一点M作椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b881044b5c73db6fcce110525741b02.png)
您最近一年使用:0次
2022-11-23更新
|
931次组卷
|
8卷引用:天津市益中学校2022-2023学年高三上学期第一次学情调研数学试题
天津市益中学校2022-2023学年高三上学期第一次学情调研数学试题内蒙古赤峰市2021届高三模拟考试数学(文)试题广东省佛山市南海区石门高级中学2020-2021学年高二下学期第一次统测数学试题江苏省盐城市四校2022-2023学年高三上学期12月联考数学试题江苏省南京市第十三中学2021届高三下学期期初数学试题(已下线)易错点13 圆锥曲线及直线与圆锥曲线位置关系-2(已下线)重难点突破15 圆锥曲线中的圆问题(四大题型)(已下线)第五篇 向量与几何 专题1 蒙日圆与阿氏圆 微点9 阿波罗尼斯圆综合训练
名校
解题方法
4 . 已知椭圆
(a>b>0)过点
,点A为椭圆的右顶点,点B为椭圆的下顶点,且|OA|=2|OB|.
(1)求椭圆的方程;
(2)过点A的直线l1与椭圆交于另一点M,过点B的直线l2与椭圆交于另一点N,直线l1与l2的斜率的乘积为
,M,N关于y轴对称,求直线l1的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38ebfa9cd052040a7bf05927ff53d075.png)
(1)求椭圆的方程;
(2)过点A的直线l1与椭圆交于另一点M,过点B的直线l2与椭圆交于另一点N,直线l1与l2的斜率的乘积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/602baac86c2b1668ecdfadc8a5948885.png)
您最近一年使用:0次
2022-01-25更新
|
853次组卷
|
8卷引用:天津市耀华中学2021-2022学年高三上学期第二次阶段检测数学试题
名校
5 . 已知椭圆
的离心率为
,其左右顶点分别为
,下焦点为
,若
.
(1)求椭圆
的方程;
(2)若点
为椭圆
上的动点,且在第一象限运动,直线
的斜率为
,且与
轴交于点
,过点
与
垂直的直线交
轴于点
,若直线
的斜率为
,求
值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57ef404abca1f78da130a38849f58559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b748f638d97ceced8b3530f709d79c48.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/415d83ba1652130790fdfaebd338c21b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2021-05-21更新
|
1233次组卷
|
3卷引用:天津市耀华中学2021-2022学年高三上学期12月第四次阶段检测数学试题
6 . 已知椭圆
:
(
)的长轴长为4,离心率为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)设椭圆
的左焦点为
,右顶点为
,过点
的直线与
轴正半轴交于点
,与椭圆交于点
,且
轴,过点
的另一直线与椭圆交于
,
两点,若
,求直线
的方程.
![](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/f89eef3148f2d4d09379767b4af69132.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7397bd90109ca5ab71e864cf91d58e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.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/d94f5f8c48d061341260119d433da51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2021-05-06更新
|
1978次组卷
|
6卷引用:天津市耀华中学2021-2022学年高三上学期第一次月考数学试题
天津市耀华中学2021-2022学年高三上学期第一次月考数学试题天津市静海区第一中学2021-2022学年高三上学期第四次阶段检测数学试题天津市河北区2021届高三一模数学试题广西玉林市育才中学2021届高三5月三模数学(文)试题(已下线)专题42 盘点圆锥曲线中的面积问题——备战2022年高考数学二轮复习常考点专题突破天津市九校2024届高三下学期联合模拟考试(一)数学试卷
名校
7 . 设
为椭圆
(
)上任一点,
,
为椭圆的左右两焦点,短轴的两个顶点与右焦点的连线构成等边三角形.
(1)求椭圆的离心率;
(2)直线
:
与椭圆交于
、
两点,直线
,
,
的斜率依次成等比数列,且
的面积等于
,求椭圆的标准方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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)
(1)求椭圆的离心率;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/675c024a32253620eda15122c5be039f.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/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/619096595112f0340a43b756e114dd3d.png)
您最近一年使用:0次
2021-03-06更新
|
823次组卷
|
4卷引用:天津市耀华中学2023届高三下学期大统练5数学试题
名校
8 . 设椭圆
的左、右焦点分别为
,左顶点为A,左焦点到左顶点的距离为1,离心率为
.
(1)求椭圆M的方程;
(2)过点A作斜率为k的直线与椭圆M交于另一点B,连接
并延长交椭圆M于点C.若
,求k的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cf6cca367ce2afd96d7d951f9587e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆M的方程;
(2)过点A作斜率为k的直线与椭圆M交于另一点B,连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/040ad5576ebe1b6940dc7932395576dc.png)
您最近一年使用:0次
2020-02-11更新
|
664次组卷
|
4卷引用:2020届天津市耀华中学高三数学上学期第一次月考数学试题