1 . 已知椭圆C的方程为
,其离心率为
,
,
为椭圆的左右焦点,过
作一条不平行于坐标轴的直线交椭圆于A,B两点,
的周长为8
(2)过B作x轴的垂线交椭圆于点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7170bb4a2ddcef39391a06c989162.png)
①试讨论直线AD是否恒过定点,若是,求出定点坐标;若不是,请说明理由.
②求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
(2)过B作x轴的垂线交椭圆于点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09e7170bb4a2ddcef39391a06c989162.png)
①试讨论直线AD是否恒过定点,若是,求出定点坐标;若不是,请说明理由.
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/372629a8666de1e9bac3e7daadcac7b6.png)
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解题方法
2 . 已知椭圆
的离心率为
,右焦点与抛物线
的焦点重合,上顶点B到直线
的距离为
.
(1)求椭圆
和抛物线
的标准方程;
(2)若直线
与椭圆
交于H,K两点,与抛物线
交于M,N两点,过点M作x轴的垂线,与直线
交于点G,点M关于点G的对称点为P,且O,N,P三点共线,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0107aa23cf707446f947fa236421c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77c7a9ead1792edf06a0f7bdb2064317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839c7616cd0d90265f4b2c9c021254fe.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af46665388a510b902827786edffaf8d.png)
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|
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解题方法
3 . 已知椭圆E的中心为坐标原点,对称轴为x轴、y轴,且过
两点.
(1)求E的方程;
(2)设过点
的直线交E于M,N两点,过M且平行于x轴的直线与线段AB交于点T,点H满足
,证明:A,H,N三点共线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea3f6d02b6ee69eba00903db57984465.png)
(1)求E的方程;
(2)设过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f57f41842628a2f1138a9f0e7939fb20.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84594e725612627ce035c87451ba3ae5.png)
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2023高二上·全国·专题练习
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解题方法
4 . 已知椭圆
的长轴为双曲线
的实轴,且椭圆
过点
.
(1)求椭圆
的标准方程;
(2)设点
是椭圆
上异于点
的两个不同的点,直线
与
的斜率均存在,分别记为
,若
,试问直线
是否经过定点,若经过,求出定点坐标;若不经过,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28675c5bcb91f9084684c58095f37ba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e4e4c7a79d9d3cdb9ac5949d53e33e.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf41eff7a1310a7dcba4b236e0543ed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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5 . 已知椭圆C:
的离心率为
,点
在椭圆上.直线
与椭圆交于
两点.且
,其中
为坐标原点.
(1)求椭圆
的方程;
(2)若过原点的直线
与椭圆
交于
两点,且过
的中点
.求四边形
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ca18783e2f3bf03b3fadd62473af700.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc11e7549cfce9220e70250ac943e457.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若过原点的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
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2023-10-06更新
|
925次组卷
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4卷引用:江苏省连云港市华杰高级中学2023-2024学年高二上学期期中数学试题
江苏省连云港市华杰高级中学2023-2024学年高二上学期期中数学试题河北省2024届高三上学期学生全过程纵向评价(一)数学试题(已下线)重难点突破17 圆锥曲线中参数范围与最值问题(八大题型)山东省滨州市惠民县2023-2024学年高二上学期期中数学试题
6 . 设椭圆
的左焦点为
,右顶点为
.
(1)求椭圆E的方程;
(2)过点
作两条斜率分别为
,
的动直线
,
分别交椭圆于点A、B、C、D,点M、N分别为线段
、
中点,若
,试判断直线
是否经过定点,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b81d7e0ae6cd2a96fa75ede38b5798.png)
(1)求椭圆E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077855b1492bf35aac52f358e5e093ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f745dbb0d0e93c05041935ea760eb50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
7 . 已知平面直角坐标系内一椭圆
,记两焦点分别为
,
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/dba55a1c-cad2-410b-a6eb-59023ff8e17b.png?resizew=222)
(1)求
的方程;
(2)设
上有三点
、
、S,直线
、
分别过
,
,连接
.
①若
,求
的面积;
②证明:当
面积最大时,
必定经过
的某个顶点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77a5b087c270dfc3f5ac18ebbc07edf3.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/9efbe4a54a27dc48e3f52d6249bd1681.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/20/dba55a1c-cad2-410b-a6eb-59023ff8e17b.png?resizew=222)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10109d34ef06c3e721fd2c7128c5b9ca.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/08cce6cac0fdd4b1a434af8bcaec8fef.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380191d5128132ab5995d3f048d3539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
②证明:当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ffd5d363ebeaa6de0ff830742643db4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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|
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|
2卷引用:江苏省苏州市2022-2023学年高二上学期期末学业质量阳光指标调研数学试题
名校
解题方法
8 . 已知过点
的椭圆
:
上的点到焦点的最大距离为3.
(1)求椭圆
的方程;
(2)已知过椭圆
:
上一点
的切线方程为
.已知点M为直线
上任意一点,过M点作椭圆
的两条切线
,
为切点,
与
(O为原点)交于点D,当
最小时求四边形
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2de52259b426acb42761fec59a7748.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知过椭圆
![](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/caf0d139c9810361b4971904a943856b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a46c2737bf9c790cdb4b767217719452.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](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/e80aa75d3d73bcd19028b3e2f9a53fce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e265894011c2b93ce5a5fa9fab2b9982.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f5534439aac6a8b23f167fefc81b929.png)
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|
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4卷引用:江苏省扬州中学教育集团树人学校2022-2023学年高三上学期期末数学试题
名校
解题方法
9 . 已知点
与
,动点
满足直线
,
的斜率之积为
,则点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)若点
在直线
上,直线
,
分别与曲线
交于点
,
,求
与
面积之比的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40630a669f4eedf626bc24851df10c85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25ce8d4a9d432afe03a988ae2d49c28c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c9355031ea0b2dc9cef3777621bc6d38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e98c4b3f3fe826e124ca7d199d4ca4b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817a419430d9951cbdb89b657b21bcf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a04e30d5827f2120d997997e4e31ba17.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db687a72ac51db994067207e136c8857.png)
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2022-11-26更新
|
1391次组卷
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5卷引用:江苏省南京市六校2022-2023学年高三上学期11月联考数学试题
江苏省南京市六校2022-2023学年高三上学期11月联考数学试题甘肃省兰州市第二十八中学2022-2023学年高二上学期期末数学试题(已下线)江苏省七市2022届高三下学期第二次调研考试数学试题变式题17-22江西省新干县第二中学2022-2023学年高二下学期3月月考数学试题重庆市长寿中学校2022-2023学年高二上学期期末数学试题
10 . 已知抛物线
的焦点与椭圆
的右焦点
重合,椭圆
的短轴长为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/db796c73-9fe2-4363-a55d-fe74f5e68e21.png?resizew=151)
(1)求椭圆
的方程;
(2)过点
且斜率为
的直线
交椭圆
于
两点,交抛物线
于
两点,请问是否存在实常数
,使
为定值?若存在,求出
的值及定值;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/384a5ece40544f0dbe0ddd07400f5295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/20/db796c73-9fe2-4363-a55d-fe74f5e68e21.png?resizew=151)
(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/f0a532e15e232cb4b99a8d4d07c89575.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8beef5e9a59a6e83f5cff1cd0ab70a60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
2022-11-18更新
|
1233次组卷
|
4卷引用:江苏省扬州市仪征中学2022-2023学年高二上学期期中数学试题