1 . 设实数
,椭圆D:
的右焦点为F,过F且斜率为k的直线交D于P、Q两点,若线段PQ的中为N,点O是坐标原点,直线ON交直线
于点M.
![](https://img.xkw.com/dksih/QBM/2021/9/6/2802454599409664/2809105175560192/STEM/7a7710a8-5cdd-4cb2-bd4d-0cb109596906.png?resizew=213)
(1)若点P的横坐标为1,求点Q的横坐标;
(2)求证:
;
(3)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fdc2518c64be54c16908f868034d8fa7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://img.xkw.com/dksih/QBM/2021/9/6/2802454599409664/2809105175560192/STEM/7a7710a8-5cdd-4cb2-bd4d-0cb109596906.png?resizew=213)
(1)若点P的横坐标为1,求点Q的横坐标;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ec1117e5c1435d4754da2114940d1d.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88326e3686b1bf8fb57d6e6d745a69ca.png)
您最近一年使用:0次
2021-09-16更新
|
993次组卷
|
3卷引用:上海市控江中学2018-2019学年高三上学期开学考试数学试题
名校
2 . 在平面直角坐标系xOy中,椭圆
,离心率
,F为椭圆左焦点.若椭圆上有一点P在x轴的上方,且
轴,线段
.
(1)求椭圆E的方程;
(2)关于椭圆E的切线有如下结论:过椭圆上一点
的切线方程
.利用此结论解决以下问题:椭圆E的左顶点为
,点D在点
处的切线上,过点D作椭圆的另一条切线DQ,切点为Q(D,Q异于顶点),直线DF与椭圆交于不同的两点M,N,过点M作x轴的垂线与直线
,
分别交于点A,B,求证:点A是线段BM的中点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99a21012ec3ed67910ffb21cef3c5ce7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c7316976a221c051a2c14df80b1347.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b1da9046b4cb82135a4a1eaa528c53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314a26fdb23ef8306dd6aecee4333234.png)
(1)求椭圆E的方程;
(2)关于椭圆E的切线有如下结论:过椭圆上一点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2752e086b85f9fbb95010bf771072af9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9656735f55e5de465e5667ba578d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e935bb9d7b7115429edbd1e7469af65.png)
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名校
解题方法
3 . 在平面直角坐标系xOy中,已知椭圆C:
长轴是短轴的
倍,点(2,1)在椭圆C上.
(1)求椭圆C的方程;
(2)设直线l与圆O:
相切,切点在第一象限,与椭圆C相交于P,Q两点.
①求证:以PQ为直径的圆经过原点O;
②若△OPQ的面积为
求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(1)求椭圆C的方程;
(2)设直线l与圆O:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
①求证:以PQ为直径的圆经过原点O;
②若△OPQ的面积为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cf68b7ab4c54fae150459b285b01aec.png)
您最近一年使用:0次
2020-11-19更新
|
2226次组卷
|
6卷引用:江苏省南京市五校2020-2021学年高二上学期10月联合调研考试数学试题
江苏省南京市五校2020-2021学年高二上学期10月联合调研考试数学试题江苏省南京市扬子二中2020-2021学年高二10月月考数学试题(已下线)黄金卷19-【赢在高考·黄金20卷】备战2021高考数学全真模拟卷(新高考专用)天津市九校联考2022届高三下学期一模数学试题天津市实验中学2022-2023学年高三上学期第二阶段学习质量检测数学试题天津大学附属中学2022-2023学年高三上学期期末数学试题
4 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff739204ba760216f82a5802e92cb244.png)
左顶点为
,离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/2020/10/10/2568028685623296/2569376604782592/STEM/7c153ce2518b468490fe7139e8a7a7ae.png?resizew=168)
(1)求
的方程;
(2)过抛物线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
上一点P的切线
交
于
两点,线段
,
的中点分别为
.求证:对任意
,都存在这样的点P,使得
所在直线平行于
轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff739204ba760216f82a5802e92cb244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e454c7161999e2a67138869f59d319b.png)
![](https://img.xkw.com/dksih/QBM/2020/10/10/2568028685623296/2569376604782592/STEM/7c153ce2518b468490fe7139e8a7a7ae.png?resizew=168)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7089148c36cb3c39af71de653756396a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次
5 . 设椭圆
,直线
,O为坐标原点.
(1)设点
在C上,且C的焦距为2,求C的方程;
(2)设l的一个方向向量为
,且l与(1)中的椭圆C交于A.B两点,求证:
为常数;
(3)设直线l与椭圆C交于A.B两点,是否存在常数k,使得
的值也为常数?若存在,求出k的表达式及
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62b67a4ee15887600fd69042a46e8514.png)
(1)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d0dec81cf9f49aaa0296828466a820.png)
(2)设l的一个方向向量为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2fc66af1e6967e988c9670ca8ceeee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cef5ef7440bb1fbb671f9c2a955497.png)
(3)设直线l与椭圆C交于A.B两点,是否存在常数k,使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cef5ef7440bb1fbb671f9c2a955497.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29cef5ef7440bb1fbb671f9c2a955497.png)
您最近一年使用:0次
名校
6 . 已知
、
分别为椭圆
的右焦点和左顶点,
,
分别在椭圆
上运动,点
,
分别在直线
,
上.
(1)若
,求
的值;
(2)记
,若直线
过点
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b36c06dce78a444b274946418c1a9ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/443aa71c19a11670ff49ec0ade3cdd16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/773184d497562ff6d2763125db0761e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277c5edd8134b666c80644af134bfa49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6e490f703eb6c9bb1278c78ebc2d661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d750d62ffb1d796460da73bfb590ace.png)
您最近一年使用:0次
2020-07-25更新
|
887次组卷
|
3卷引用:2020年普通高等学校招生伯乐马模拟考试(五)数学(理)试题
7 . 已知平面内动点
与点
,
连线的斜率之积为
.
(1)求动点
的轨迹
的方程;
(2)过点
的直线与曲线
交于
,
两点,直线
,
与直线
分别交于
,
两点.求证:以
为直径的圆恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/852b303689c31189cd47bb4a3220f9fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d78fd95f89dec2d373fa57f02acd739f.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2ba2238d6afe0187534155dd9ac48c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.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/411461db15ee8086332c531e086c40c7.png)
您最近一年使用:0次
2020-06-25更新
|
896次组卷
|
2卷引用:河南省洛阳市2020届高三第三次统一考试 数学(理)试题
解题方法
8 . 已知椭圆
过点
,
分别为椭圆C的左、右焦点且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/bc8d2ac0-fbb5-4154-b55d-353165a57a56.png?resizew=229)
(1)求椭圆C的方程;
(2)过P点的直线
与椭圆C有且只有一个公共点,直线
平行于OP(O为原点),且与椭圆C交于两点A、B,与直线
交于点M(M介于A、B两点之间).
(i)当
面积最大时,求
的方程;
(ii)求证:
,并判断
,
的斜率是否可以按某种顺序构成等比数列.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8989cd07bd3d5f89627c3acb24c0a462.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/4/bc8d2ac0-fbb5-4154-b55d-353165a57a56.png?resizew=229)
(1)求椭圆C的方程;
(2)过P点的直线
![](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/707ea658f3a9359f5740d5aab48f7948.png)
(i)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(ii)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb53c7cc8aac84b2ae3ef769bb46adb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790ef3382b1c731f2885eecfd92c2a86.png)
您最近一年使用:0次
2020-06-11更新
|
1703次组卷
|
7卷引用:山东省潍坊市2020届高三模拟(二模)数学试题
山东省潍坊市2020届高三模拟(二模)数学试题山东省平邑县第一中学2020届高三下学期第八次调研考试数学试题(已下线)数学-6月大数据精选模拟卷03(上海卷)(满分冲刺篇)(已下线)专题十 平面解析几何-山东省2020二模汇编山东省泰安市2020-2021学年高三上学期1月月考数学试题(已下线)专题21 椭圆、双曲线、抛物线的几何性质的应用(讲)-2021年高三数学二轮复习讲练测(新高考版)(已下线)专题25 椭圆、双曲线、抛物线的几何性质的应用(讲)-2021年高三数学二轮复习讲练测(文理通用)
名校
解题方法
9 . 已知椭圆C:
的离心率为
,
的面积为2.
(I)求椭圆C的方程;
(II)设M是椭圆C上一点,且不与顶点重合,若直线
与直线
交于点P,直线
与直线
交于点Q.求证:△BPQ为等腰三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e7b2b6af06d9e4b151e93ae9fc688f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f737029b90a384c2b48973b84bfe74b8.png)
(I)求椭圆C的方程;
(II)设M是椭圆C上一点,且不与顶点重合,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e26d9636ad77369535852c6e4493446a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c2cc110e46ae4b3432814810e28bcf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9399c9a2a31b0e3165aea2d6ccc4f7c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/668438e15423368cd744445e824d18a1.png)
您最近一年使用:0次
2020-05-09更新
|
1914次组卷
|
9卷引用:2020届北京市海淀区高三一模数学试题
2020届北京市海淀区高三一模数学试题黑龙江省哈尔滨市哈尔滨师范大学附属中学2020-2021学年高二上学期期末考试 数学(文)试题北京市第五十七中学2021-2022学年高二上学期期末数学试题北京市第五中学2022届高三下学期三模数学试题四川省成都石室中学2022-2023学年高三上学期一诊模拟考试数学(文科)试题四川省成都石室中学2022-2023学年高三上学期一诊模拟考试数学(理科)试题陕西省实验中学2023届高三上学期第四次模拟考试理科数学试题陕西省实验中学2023届高三上学期第四次模拟考试文科数学试题黑龙江省哈尔滨德强学校2022-2023学年高三下学期清北班阶段性测试(开学考试)数学试卷
解题方法
10 . 已知椭圆
的中心为坐标原点
,焦点在
轴上,离心率为
,
分别为椭圆
的左、右焦点,点
在椭圆
上,以线段
为直径的圆经过点
,线段
与
轴交于点
,且
.
(1)求椭圆
的方程;
(2)设动直线
与椭圆
交于
两点,且
.求证:动直线
与
圆相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/643ef7d761de0e794fc39937dc72ac6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da01a3abe1c9dc4e6283afa0dc1a0d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05f2188d99b44972f1e13d3a339ee5c7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设动直线
![](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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc2abe13e2d4176f55f71677bbbb6eb4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2845cff59808d0945644a6c867e40740.png)
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