名校
解题方法
1 . 已知点
是椭圆
的右焦点,椭圆上一点
关于原点的对称点为
,若
的周长为
,则椭圆的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1294434b22cb5133043a2270ae1c43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/004104bafb5f30338123d4ea2b7fedde.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec71a2efdbd011352326c1d2d9992bd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆W:
的离心率为
,左、右焦点分别为
,
,过
且垂直于x轴的直线被椭圆W所截得的线段长为
.
(1)求椭圆W的方程;
(2)直线
与椭圆W交于A,B两点,连接
交椭圆W于点C,若
,求直线AC的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.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/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9868f77d5ab5073b6145f1c6d272122e.png)
(1)求椭圆W的方程;
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa841ce5d58b64f747a3c1b69bb20a5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6950900f2551c9b195f16d617275adfe.png)
您最近一年使用:0次
2022-11-23更新
|
336次组卷
|
7卷引用:安徽省黄山市“八校联盟”2022-2023学年高二上学期11月期中考试数学试题
3 . 已知命题
对
恒成立,命题
方程
表示的曲线为焦点在
轴上的椭圆,且
为真命题,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfb4a793681a64af1f894584f677b445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c780149aef1bd77162e85f7f8906a6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce20ef9c08e82df8c7f45bac6dd31d36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aac2759c82d304966e0de7237dd8e331.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f675824e539f50cec53120959d32e554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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解题方法
4 . 已知椭圆
的左、右焦点分别是
,过点
的直线
与椭圆相交于
两点,且
的周长为
.
(1)求椭圆
的标准方程;
(2)在椭圆中有这样一个结论“已知
在椭圆
外 ,过
作椭圆的两条切线,切点分别为
,则直线
的方程为
”.现已知
是圆
上的任意点,
分别与椭圆
相切于
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f49644cd9fa4688cc3a74a234952530.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5eb2485f90dbfd0dfd6e7d179a856f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在椭圆中有这样一个结论“已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4127b796482b8d004203662147aac499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf9f50605db5d5f8f3a01ee8e474a112.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5425108c557f0f21474c045334f97d9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4a949c00526fddf435423272cf10f25.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49137970108f50350a3211aa0281faaf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03df57efff473b3cfeb8503796b7d6b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
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名校
解题方法
5 . 已知椭圆
的左右焦点分别为
和
,由4个点
、
、
和
组成了一个高为
,面积为
的等腰梯形.
(1)求椭圆的方程;
(2)过点
的直线和椭圆交于两点
,求△
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.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/6d17c3d193e1ba84607e93c5ca4be12c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6134983a8decef61d715c3eedb9f31.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/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/adbd3e8cf8325999cde03adf845d3dd0.png)
(1)求椭圆的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dec9325ab8b0f7016c011d1c37d5c25a.png)
您最近一年使用:0次
2020-12-25更新
|
136次组卷
|
4卷引用:安徽省黄山市屯溪第一中学2020-2021学年高二下学期期中文科数学试题
解题方法
6 . 在平面直角坐标系
中,已知椭圆C:
的左焦点
坐标为
,
分别为椭圆C的左、右顶点,过左焦点
的直线
交椭圆C于
两点(其中
在
轴上方),当直线
垂直于
轴时,
.
(1)求椭圆C的标准方程;
(2)若
与
的面积之比为1:7,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/bc6554ac3dff4a59833e407db887f6e6.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/ddafc7d1c71c9c77e54f8d353117f858.png)
(1)求椭圆C的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c105d6ba18fbb0581fb982175e2eac9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7e64c953aaf341e772a5fe776fbc78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
7 . 椭圆
的左、右焦点分别为
,
,过点
的直线
与椭圆交于点
,
,
的周长为
.
(1)求椭圆的标准方程;
(2)若
.①当
时,求直线
的方程;
②证明
是定值,并求出此定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b5e56b5cbcf69756792fc934bcc20cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e2031d209711b058f3d278ede3c1d33.png)
(1)求椭圆的标准方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d5b5ffa67d3729bf5508eccb1b2af8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f15169f63977b2de3cc944fb6e97bc3.png)
您最近一年使用:0次
2020-01-30更新
|
156次组卷
|
2卷引用:安徽省黄山市2019-2020学年高二上学期期末数学(理)试题
名校
8 . 阿基米德(公元前287年—公元前212年)不仅是著名的物理学家,也是著名的数学家,他利用“逼近法”得到椭圆的面积除以圆周率等于椭圆的长半轴长与短半轴长的乘积.若椭圆C的焦点在x轴上,且椭圆C的离心率为
,面积为12
,则椭圆C的方程为( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/059d02ae074c7c2f7dfde8058dfa55ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-11-19更新
|
1210次组卷
|
11卷引用:安徽省黄山市2020-2021学年高二上学期期末数学(文)试题
安徽省黄山市2020-2021学年高二上学期期末数学(文)试题辽宁省六校协作体2019-2020学年高二上学期期中数学试题江西省吉安市五校2019-2020学年高二上学期第二次联考数学(理)试卷陕西省商洛市商丹高新学校2019-2020学年高二上学期11月质量检测数学(理)试题黑龙江省大庆铁人中学2020-2021学年高二上学期期中考试数学试题黑龙江省大庆市铁人中学2020-2021学年高二(上)期中数学试题福建省华安县第一中学2020-2021学年高二上学期期中考试数学试题辽宁省六校协作体2020-2021学年高二第一学期期中考试数学试题江苏省扬州市邗江区2021-2022学年高二上学期期中数学试题宁夏回族自治区银川市兴庆区银川一中2019-2020学年高三第五次月考数学(理)试题吉林省通钢一中、集安一中、梅河口五中等联谊校2019-2020学年高三下学期第五次月考数学(理)试题
名校
9 . 若椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
是以双曲线
的顶点为焦点,以其焦点为顶点.
(Ⅰ)求椭圆
的方程;
(Ⅱ)若
是椭圆
上的一点,
、
是椭圆
的两焦点,且
,求
的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a218602e8e3a52f74f760059aa7014.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)若
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04f9bdc6d9f09e14b037ea7d3ee1f623.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42660cf98c653f12ebd2e960458f7441.png)
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2019-01-27更新
|
323次组卷
|
2卷引用:【市级联考】安徽省黄山市2018-2019学年高二上学期期末考试数学(文)试题
名校
10 . 设
且
,则方程
和方程
,在同一坐标系下的图象大致是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fb5f717bbedf81e6b02bb8d594d486.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32711fd633174bc251cb9525615d9317.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1611588961360b74506644dbaaf8fc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e9966cb42839dc07e87c7cd05c820b0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2019-04-03更新
|
876次组卷
|
8卷引用:安徽省黄山市2017-2018学年高二上学期期末考试数学(理)试题
安徽省黄山市2017-2018学年高二上学期期末考试数学(理)试题【全国百强校】四川省雅安中学2018-2019学年高二下学期第一次月考数学(文)试题四川省攀枝花市第十五中学2019-2020学年高二上学期第一次月考数学文科试题山西省怀仁市第一中学云东校区2020-2021学年高二上学期第三次月考数学(理)试题江苏省南通市如皋市第一中学2020-2021学年高二上学期9月调研数学试题湖北省武汉中学2021-2022学年高二上学期12月月考数学试题2023版 北师大版(2019) 选修第一册 名师精选卷 第二章 圆锥曲线2023版 苏教版(2019) 选修第一册 名师精选卷 第三章 圆锥曲线与方程