解题方法
1 . 已知椭圆
,
为椭圆
的右焦点,
为椭圆上一点,
的离心率![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/d0a71a8a-5397-4321-8b4b-b65c0605a510.png?resizew=189)
(1)求椭圆
的标准方程;
(2)斜率为
的直线
过点
交椭圆
于
两点,线段
的中垂线交
轴于点
,试探究
是否为定值,如果是,请求出该定值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e0a9fa53090c853a0ebf4d5efecda4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/10/d0a71a8a-5397-4321-8b4b-b65c0605a510.png?resizew=189)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率为
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c987142aad34adcd31a6eefd6608d1c1.png)
您最近一年使用:0次
名校
解题方法
2 . 已知椭圆E:
的左、右焦点分别为F1,F2,离心率为
,点A在椭圆E上,∠F1AF2=60°,△F1AF2的面积为4
.
(1)求椭圆E的方程;
(2)过原点O的两条互相垂直的射线与椭圆E分别交于P,Q两点,证明:点O到直线PQ的距离为定值,并求出这个定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a625c499f51d7320ce4fecb49e76adf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆E的方程;
(2)过原点O的两条互相垂直的射线与椭圆E分别交于P,Q两点,证明:点O到直线PQ的距离为定值,并求出这个定值.
您最近一年使用:0次
2020-02-21更新
|
242次组卷
|
2卷引用:河北省邢台市2018-2019学年高二上学期期末数学(理)试题
名校
解题方法
3 . 如图所示,已知A、B、C是长轴长为4的椭圆E上的三点,点A是长轴的一个端点,BC过椭圆中心O,且
,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/33a590f2-2b2b-4297-b6e1-9de8f49e1d48.png?resizew=198)
(Ⅰ)求椭圆E的方程;
(Ⅱ)设
是以原点为圆心,短轴长为半径的圆,过椭圆E上异于其顶点的任一点P,作
的两条切线,切点分别为M,N,若直线MN在x轴、y轴上的截距分别为m,n,试计算
的值是否为定值?如果是,请给予证明;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/927599c5937ce806a0bedbe0192b1095.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffd69522689b9418afd0c85a858322dd.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/33a590f2-2b2b-4297-b6e1-9de8f49e1d48.png?resizew=198)
(Ⅰ)求椭圆E的方程;
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81717125fadcf1b65daddd2f216731c8.png)
您最近一年使用:0次
4 . 已知椭圆
的离心率
,且椭圆过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8da36e3081bfe5d32c9ec70be4da3da.png)
(1)求椭圆
的标准方程;
(2)设直线
与
交于
、
两点,点
在椭圆
上,
是坐标原点,若
,判定四边形
的面积是否为定值?若为定值,求出该定值;如果不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075ba8c6fb5ef7288cd3fed425c8e69e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8da36e3081bfe5d32c9ec70be4da3da.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c8bd916b5945fee04c1acb26f8ac86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7346144de4c74f6b8bb14bea9ebd41.png)
您最近一年使用:0次
2020-02-18更新
|
4222次组卷
|
21卷引用:【市级联考】湖南省郴州市2019届高三第三次质量检测数学(文)试题
【市级联考】湖南省郴州市2019届高三第三次质量检测数学(文)试题【市级联考】陕西省榆林市2019届高三第四次普通高等学校招生模拟考试文科数学试题2020届河南省南阳市高三上学期期末数学(理)试题2020届河南省信阳市高三第二次教学质量检测数学(理)试题2019届湖南省长沙市雅礼中学高三下学期5月月考数学(文)试题2019届陕西省榆林市高三第四次模拟考试数学(文)试题(已下线)提升套餐练05-【新题型】2020年新高考数学多选题与热点解答题组合练(已下线)冲刺卷05-决战2020年高考数学冲刺卷(山东专版)2019届吉林省普通高三第三次联合模拟数学(文)试题2020届河南省开封市第五中学高三第四次教学质量检测数学(理)试卷(已下线)专题31 圆锥曲线中的定点、定值、探索性问题-冲刺2020高考跳出题海之高三数学模拟试题精中选萃(已下线)专题06 解析几何中的定点、定值问题(第五篇)-备战2020年高考数学大题精做之解答题题型全覆盖2020届黑龙江省大庆实验中学高三第一次模拟数学(文)试题河南省信阳市2020届高三上学期第二次教学质量检测(期末)数学(文)试题湖南省邵阳市邵东县第一中学2020-2021学年高三上学期第二次月考数学试题湖南省长沙市明德中学2019-2020学年高二上学期期中数学试题江西省信丰中学2021-2022学年高二下学期第一次月考数学(理)B层试题苏教版(2019) 选修第一册 选填专练 第3章 微专题七 高考中圆锥曲线问题(3):证明与探索性问题河南省许平汝联盟2021-2022学年高三下学期4月模拟考试文科数学试题河南省鹤壁市浚县第一中学2021-2022学年高三下学期4月考试文科数学试题宁夏中卫市中宁县2022-2023学年高二上学期质量测查(期末)数学(理)试题
名校
解题方法
5 . 已知椭圆
(
)的上顶点为
,左焦点为
,离心率为
,直线
与圆
相切.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/d29c3e71-142e-4cd5-a45e-f9c10324a489.png?resizew=183)
(1)求椭圆
的标准方程;
(2)设过点
且斜率存在的直线
与椭圆
相交于
两点,线段
的垂直平分线交
轴于点
,试判断
是否为定值?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7d72a07a4e5acfc140a3cea1f26b951.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b28123e129b6426c9a5f31ad8ec2465b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/27/d29c3e71-142e-4cd5-a45e-f9c10324a489.png?resizew=183)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设过点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/252531955c6872a2764fbeea4ec8a557.png)
您最近一年使用:0次
2020-02-12更新
|
755次组卷
|
3卷引用:2020届江西省九江市高三第一次模拟数学理科试题
名校
6 . 已知椭圆
上一点
,一条直线
与
平行且与椭圆交于
、
两点,直线
、
分别与
轴正半轴交于
、
两点,求
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99e4a41cbe3d1f25154602dee11d36ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/1933a98a5b1d907239c59a43233e30e6.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
7 . 已知椭圆
(
)的左右焦点分别为
,
,已知其离心率为
,且过点
.
(1)求椭圆的标准方程.
(2)设
,
是椭圆上位于
轴上方的两点,且直线
与直线
平行,
与
交于点
,探究
是否为定值?如果为定值,请求出该定值;如果不为定值,请说明理由.
![](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/5076829e649b3f3866d4a7e07a5713e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697c20fca284394bf5d5b9e5f6d952e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03efa0031095d2186f68e407859eb37d.png)
(1)求椭圆的标准方程.
(2)设
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cabea664e61863b3b3279dbce607924e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3656055f5256cd06e636ea96e9f89c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbad65b3d744b70da2480eee1cdb587.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bfe1cad1ce47339827ac5047af4647d.png)
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名校
8 . 已知椭圆
的离心率为
,其右顶点为
,下顶点为
,定点
,
的面积为
,过点
作与
轴不重合的直线
交椭圆
于
两点,直线
分别与
轴交于
两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/ffb79f4d-9789-42fb-bf3a-88e8f5d6224a.png?resizew=190)
(1)求椭圆
的方程;
(2)试探究
的横坐标的乘积是否为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.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/b5558ffa6dc28d437c0467c7f361d444.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ca7d1107389675d32b56ec097464c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa154ac33703b5c836047b2143697c6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/23/ffb79f4d-9789-42fb-bf3a-88e8f5d6224a.png?resizew=190)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)试探究
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
您最近一年使用:0次
2020-01-11更新
|
1318次组卷
|
9卷引用:2020年1月江西省上饶市一模拟数学(理科)试题
2020年1月江西省上饶市一模拟数学(理科)试题湖南省衡阳市第一中学2020-2021学年高三上学期第一次月考数学试题江苏省泰州中学2020-2021学年高二上学期10月质量检测数学试题湖南省长沙市雅礼中学2020-2021学年高三上学期月考(三)数学试题山东省临沂市2020-2021学年高二上学期期末数学试题福建省宁化第一中学2021-2022学年高二上学期第一次阶段考试数学试题福建省泉州第一中学2022届高三上学期期中考试数学试题(已下线)专题16 圆锥曲线常考题型04——定值问题-【重难点突破】2021-2022学年高二数学上册常考题专练(人教A版2019选择性必修第一册)广东省揭阳市揭西县河婆中学2022届高三下学期综合测试(二)数学试题
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9 . 已知椭圆
:
,长半轴长与短半轴长的差为
,离心率为
.
(1)求椭圆
的标准方程;
(2)若在
轴上存在点
,过点
的直线
分别与椭圆
相交于
、
两点,且
为定值,求点
的坐标.
![](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/47cfe4e08c06bde245e58aa22485044c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若在
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/0f85fca60a11e1af2bf50138d0e3fe62.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/537a720ac4508b5ba43279509bb02176.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-01-03更新
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418次组卷
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7卷引用:江西省赣州市2019-2020学年高二上学期12月月考数学(理)试题
名校
10 . 已知椭圆C:
+y2=1,不与坐标轴垂直的直线l与椭圆C相交于M,N两点.
(1)若线段MN的中点坐标为 (1,
),求直线l的方程;
(2)若直线l过点P(p,0),点Q(q,0)满足kQM+kQN=0,求pq的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de95471bb6c16acb4fd84d8315e6a637.png)
(1)若线段MN的中点坐标为 (1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(2)若直线l过点P(p,0),点Q(q,0)满足kQM+kQN=0,求pq的值.
您最近一年使用:0次