1 . 已知
是椭圆
的左、右焦点,点
在椭圆上,
为椭圆的离心率,且点
为椭圆短半轴的上顶点,
为等腰直角三角形.
(1)求椭圆的标准方程;
(2)过点
作不与坐标轴垂直的直线
,设
与圆
相交于
两点,与椭圆相交于
两点,当
且
时,求
的面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8bc2e446c81e5820782b48dc0e539535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a90c19c80e3cae271b3c9813ec19ccac.png)
(1)求椭圆的标准方程;
(2)过点
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/833bf16f0161259e9d973dbdd5c6b18c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0747aa7b72b3a0ed18647163a55ce18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51b2c06293c841d2216f43131ac541dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/479905259def78f7f344d2e14302fe27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2017-04-27更新
|
913次组卷
|
3卷引用:河北省定州中学2018届高三上学期第二次月考数学试题
2 . 如图,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
左、右顶点为
、
,左、右焦点为
、
,
,
.直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
交椭圆于点
,
两点,与线段
、椭圆短轴分别交于
、
两点(
,
不重合),且
.
![](https://img.xkw.com/dksih/QBM/2017/4/6/1660112344940544/1660158961303552/STEM/23ac8d70eb7844d58a953611f4d25975.png?resizew=124)
(1)求椭圆
的方程;
(2)设直线
,
的斜率分别为
,
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2080eb912204afa61eacb971b7593438.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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70964b810dc1ed0cc62a07204877dbb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1259a058f58ee3f83300b5f55b80c8da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15b256345d7109e081b7c895591e995d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41169a9e434e7dc1bb21efb32520e4f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/495f737a5532611da8a94ad16abf3ab8.png)
![](https://img.xkw.com/dksih/QBM/2017/4/6/1660112344940544/1660158961303552/STEM/23ac8d70eb7844d58a953611f4d25975.png?resizew=124)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.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/67351fe10fcfc3f9072eec4c60bfaaa5.png)
您最近一年使用:0次
2017-03-30更新
|
908次组卷
|
2卷引用:2017届河北省衡水中学高三下学期三调考试数学(理)试卷
名校
3 . 已知椭圆
:
的四个顶点组成的四边形的面积为
,且经过点
.
![](https://img.xkw.com/dksih/QBM/2019/3/23/2166836469366784/2168057961062400/STEM/430bea2feb9549dfb1c6dc293ca12e2e.png?resizew=193)
(1)求椭圆
的方程;
(2)若椭圆
的下顶点为
,如图所示,点
为直线
上的一个动点,过椭圆
的右焦点
的直线
垂直于
,且与
交于
,
两点,与
交于点
,四边形
和
的面积分别为
,
,求
的最大值.
![](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/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe8530b8e246a9a5ec9fe3b9c347d5a.png)
![](https://img.xkw.com/dksih/QBM/2019/3/23/2166836469366784/2168057961062400/STEM/430bea2feb9549dfb1c6dc293ca12e2e.png?resizew=193)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若椭圆
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64b67f38247dea57c3167f02de51cf3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb556e962e111e59c345be7240e202c0.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/50524aaa1503092bd18419de6d851541.png)
您最近一年使用:0次
2016-12-04更新
|
3039次组卷
|
8卷引用:河北省衡水中学2018届高三上学期八模考试数学(理)试题
解题方法
4 . 如图所示,已知椭圆的中心在原点,焦点在
轴上,长轴长是短轴长的2倍且经过点
,平行于
的直线
在
轴上的截距为
,直线
交椭圆于
两个不同点.
(1)求椭圆的方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85d23fc512ad69a2d5919ce690407704.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](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/87484a879f450ab097f720fb2a0f4a2f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/8/7/77f626cd-3a0a-4cf4-bd3d-2e7aa8898417.png?resizew=197)
您最近一年使用:0次
2016-12-04更新
|
516次组卷
|
6卷引用:2015-2016学年河北秦皇岛卢龙县高二下学期期末数学(文)试卷
名校
解题方法
5 . 已知椭圆
过点
,离心率为
,点
分别为其左右焦点.
(1)求椭圆
的标准方程;
(2)若
上存在两个点
,椭圆上有两个点
满足
三点共线,
三点共线,且
,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2f2d391b1e6304eb2bba560d0ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd670bd3726ea58ab5c46c245d05559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d676ff4bf2f8e136835a0a702ebe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c485045b8cc718cfabee23fe984f82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86859f48d33b5163960bef221b189b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99393efa04579f3db5cf4f7e319f0440.png)
您最近一年使用:0次
2016-12-03更新
|
1437次组卷
|
6卷引用:2016届河北省正定中学高三上学期期中数学试卷
解题方法
6 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)不垂直与坐标轴的直线
与椭圆
交于
两点,线段
的垂直平分线交y轴于点
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e684712aade8dcebb62716843791034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不垂直与坐标轴的直线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff26171e5cdbb425f8c7642f3a1ec7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe17db75cdacde06262271d174307d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
9-10高二下·河南郑州·期末
解题方法
7 . 设
分别为椭圆
的左、右两个焦点.
(1)若椭圆
上的点
到
两点的距离之和等于4,求椭圆
的方程和焦点坐标;
(2)设点P是(1)中所得椭圆上的动点,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315a24a74c99dfa18e6d8b1b5220724b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点P是(1)中所得椭圆上的动点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f274a6fb62ddc16a07565d54006985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2016-12-03更新
|
578次组卷
|
5卷引用:2015-2016学年河北省望都中学高二10月月考文科数学试卷
2015-2016学年河北省望都中学高二10月月考文科数学试卷(已下线)郑州智林学校09-10学年高二下学期期末考试数学试卷(理科)(已下线)2011-2012年福建省福州市八中高二上学期期末考试理科数学2014-2015学年甘肃省兰州一中高二上学期期末考试数学试卷2016-2017学年山东桓台二中高二9月月考数学试卷
11-12高二下·河北衡水·阶段练习
8 . 已知抛物线
的焦点
以及椭圆
的上、下焦点及左、右顶点均在圆
上.
(1)求抛物线
和椭圆
的标准方程;
(2)过点
的直线交抛物线
于
、
两不同点,交
轴于点
,已知
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c518a09919976d184de6ee1c5dec4b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83de9a16fe69aa19744801693652be7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
(1)求抛物线
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/93f38efbc14041c2be89dc0577ab8df8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/e966c9fed75c4e6181a62c4a5cc261d9.png)
(2)过点
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/769ad5ed395a48ca932943309bed59dc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/93f38efbc14041c2be89dc0577ab8df8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/acf674bda8a3497bb8c2cf93bd59f47e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/55bd1e65687c4ff9b4d387dbcdebfdec.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/3491c81e10734d34b9b8c3e86933f59b.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/fd413e6d44a24a3ba27eda3145770c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8887db8acd21bcb971ccf7f56ef1935f.png)
您最近一年使用:0次