1 . 如图,在平面直角坐标系xOy中;已知椭圆
的焦距为2,一条准线方程为
,设过右焦点F任意作一条直线l交椭圆E于M,N两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/b6a2dc95-48fd-4113-995f-7b18f571802d.png?resizew=181)
(1)求椭圆E的标准方程;
(2)若直线l的斜率为1,求弦长MN的值;
(3)设点P在线段MN上运动,右顶点A关于点P的对称点为点C,求四边形AMCN面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/b6a2dc95-48fd-4113-995f-7b18f571802d.png?resizew=181)
(1)求椭圆E的标准方程;
(2)若直线l的斜率为1,求弦长MN的值;
(3)设点P在线段MN上运动,右顶点A关于点P的对称点为点C,求四边形AMCN面积的最大值.
您最近一年使用:0次
名校
解题方法
2 . 设
为椭圆
在第一象限上的点,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/914075a4574c09bdb860d8f8f09a4e7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f6684b26e394132206437aa6e6cf3c8.png)
您最近一年使用:0次
2020-04-17更新
|
332次组卷
|
2卷引用:2019届江苏省南京大学附属中学高三三模数学试题
名校
解题方法
3 . 如图,已知四棱锥
的底面是菱形,对角线
,
交于点
,
,
,
,
底面
,设点
满足
.
![](https://img.xkw.com/dksih/QBM/2020/4/16/2442972162203648/2443665956724736/STEM/05ae41ba23a548d9b3901fb533e4333d.png?resizew=174)
(1)若
,求二面角
的大小;
(2)若直线
与平面
所成角的正弦值
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0585b6c0f156eecf9662b9846d4eb693.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f561a36cc4c9293d8a63ee4e1a7146b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55e2857963e3ea3578e9a13638c3a2c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02672185596d0be60de9e2e93afb59e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bbc6f007dbf1c1a36eb031e520608403.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75ff968fd0709d072c7a4b7000a411e4.png)
![](https://img.xkw.com/dksih/QBM/2020/4/16/2442972162203648/2443665956724736/STEM/05ae41ba23a548d9b3901fb533e4333d.png?resizew=174)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac1c3ea872a20fdc1843cb5ffce8a554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e9ac46aabe38e5ea1a8cb0febc98af.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7bc46688d8723cf2003fc25890265200.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d83fb9ac8a18e78a4c56da79514b5ccb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2020-04-17更新
|
1290次组卷
|
5卷引用:江苏省扬州市高邮市2018-2019学年高二下学期期中数学(理)试题
江苏省扬州市高邮市2018-2019学年高二下学期期中数学(理)试题江苏省镇江市扬中市第二高级中学2020-2021学年高三上学期初检测数学试题重庆市暨华中学2020-2021学年高二上学期第二次月考数学试题辽宁省抚顺市抚顺县高级中学校2021-2022学年高二上学期10月月考数学试题(已下线)专题4.1 第一、二章(空间向量与立体几何、直线和圆的方程)阶段检测-【满分计划】2021-2022学年高二数学阶段性复习测试卷(人教A版2019选择性必修第一册)
名校
4 . 已知双曲线C的方程是:
(
,
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19f3fa0b40fb0d9b8c62e37316ab3b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
A.当![]() ![]() |
B.过双曲线C右焦点F的直线与双曲线只有一个交点的直线有且只有2条; |
C.过双曲线C右焦点F的直线与双曲线右支交于M,N两点,则此时线段![]() |
D.双曲线C与双曲线:![]() ![]() ![]() |
您最近一年使用:0次
解题方法
5 . 在平面直角坐标系
中,点
,过动点
作直线
的垂线,垂足为
,且
.记动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
的直线
交曲线
于不同的两点
,
.
①若
为线段
的中点,求直线
的方程;
②设
关于
轴的对称点为
,求
面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a089c207e39a24d0d82aa853ac2bbb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f9f60c8240c956ef340ca4b9ee8c59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②设
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9f8f01137e92c0f2e63467036ae9cce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2020-04-06更新
|
785次组卷
|
3卷引用:江苏省南京市2019-2020学年高二上学期期中数学试题
名校
6 . 平面直角坐标系xOy中,已知椭圆C:
的离心率为
,且点
在椭圆C上.椭圆C的左顶点为A.
(1)求椭圆C的方程
(2)椭圆的右焦点且斜率为
的直线与椭圆交于P,Q两点,求三角形APQ的面积;
(3)过点A作直线与椭圆C交于另一点B.若直线
交
轴于点C,且
,求直线
的斜率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed6b9540857e386651e191a0a5b5a98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d695d4b8eb4f37c2c1bf46a190d461a4.png)
(1)求椭圆C的方程
(2)椭圆的右焦点且斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
(3)过点A作直线与椭圆C交于另一点B.若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83ff26eeabfaef6e944082999e39e814.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-04-06更新
|
504次组卷
|
3卷引用:江苏省苏州市吴江区2019-2020学年高三上学期第二次月考数学试题
名校
解题方法
7 . 已知椭圆
的左右焦点分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
,上顶点为B,离心率为e,点P在椭圆上(异于点B).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
及
,求
的取值范围;
(2)记直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
的斜率分别为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
,若
,且
,求椭圆C的离心率.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c84d316b10430afac5b0c065f31e1b2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/23/b021f21c-8786-4848-8971-fc37ef43da6a.png?resizew=162)
(1)若椭圆C经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33c3988d58a90ce85be4e65c4a86de45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12604a5a6371ddb77722d04006f5d5eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b51ba4eb57c3dad6a9356d4b70dc384.png)
(2)记直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c12279880baa3b90297797bf4d29a265.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c83e02c09428538ce8ae136cff26d3f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c87cef1d0bd8b2ee3476a5fa4dbbdc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2bf1ac7607f9d0a1639ec59757aca5d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ad7dcfc3e70b0b4c3c93136252b9037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db821941a51ba432ffad4ba5cb253cfc.png)
您最近一年使用:0次
8 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且椭圆
短轴的一个顶点到左焦点
的距离等于
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
的方程;
(2)设经过点
的直线
交椭圆
于
两点,弦
的中垂线
交
轴于点
.
①求实数
的取值范围;
②若
,求实数
的值.
![](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/8d5989c84e320b504511f23eeb6e7357.png)
![](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/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/5/7b121abd-0a84-4905-aed8-dd148b0b6048.png?resizew=235)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bacfc149ede71417fa599c21b5a84cb8.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2da6ef88591589f330304297d3abfcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38f4ea4bc4c655fd337f8bdd18c493b5.png)
①求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12c7613bc5c3fc3d8d20b8652fedc736.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79b752f0f189e5d8666daea73e145dff.png)
您最近一年使用:0次
名校
解题方法
9 . 在平面直角坐标系
中,椭圆
:
(
)的离心率为
,焦点到相应准线的距离为
,动直线l与椭圆交于
两点.
(1)求椭圆
的标准方程;
(2)若
,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fd2981bf2261343f905ec1b5355a3c4.png)
您最近一年使用:0次
2020-03-26更新
|
712次组卷
|
2卷引用:2019届江苏省无锡市第一中学高三下学期2月期初考试数学试题
10 . 平面直角坐标系
中,椭圆C:
(
)左,右焦点分别为
,
,且椭圆的长轴长为
,右准线方程为
.
(1)求椭圆C的方程;
(2)设直线l过椭圆C的右焦点
,且与椭圆相交与A,B(与左右顶点不重合)
(i)椭圆的右顶点为M,设
的斜率为
,
的斜率为
,求
的值;
(ii)若椭圆上存在一点D满足
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/e82fe25db889399bb3ca4ffd5dd5db84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dff1e33966ff01e4a394b42a3c65a400.png)
(1)求椭圆C的方程;
(2)设直线l过椭圆C的右焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a61d572ecf27dc02fcbd588f24647b1d.png)
(i)椭圆的右顶点为M,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2562424a83aae7e4b3f8adf90307961a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e5c62f22d7afc5627fcb86599faa8e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03b58edb637c5dfa03794f3952de9d83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2bb6eabffd165f9580e9dcaaace3a89.png)
(ii)若椭圆上存在一点D满足
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2738e9e0593d33af7d7177c50e0036a.png)
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