1 . 在平面直角坐标系xOy中:①已知点A(
,0),直线
,动点P满足到点A的距离与到直线l的距离之比
;②已知点S,T分别在x轴,y轴上运动,且|ST|=3,动点P满
;③已知圆C的方程为
直线l为圆C的切线,记点
到直线l的距离分别为
动点P满足
(1)在①,②,③这三个条件中任选-一个,求动点P的轨迹方程;
(2)记(1)中动点P的轨迹为E,经过点D(1,0)的直线l’交E于M,N两点,若线段MN的垂直平分线与y轴相交于点Q,求点Q纵坐标的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af3a8183f5256dbe27e2fd7e3f4873e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6936c7b80f931a7d4905f3d62bbef1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e95ee64c7b477a12bf992ea5115b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/970367bb69407fee68e48a4f4219f4cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da92abfa21a615875f91ab817c4a40c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e38379156c366519e3aca6b7fa84e08.png)
(1)在①,②,③这三个条件中任选-一个,求动点P的轨迹方程;
(2)记(1)中动点P的轨迹为E,经过点D(1,0)的直线l’交E于M,N两点,若线段MN的垂直平分线与y轴相交于点Q,求点Q纵坐标的取值范围.
您最近一年使用:0次
2021-06-03更新
|
1591次组卷
|
11卷引用:山东省日照市第一中学2020届高三下学期模拟考试数学试题
山东省日照市第一中学2020届高三下学期模拟考试数学试题(已下线)专题十 平面解析几何-2020山东模拟题分类汇编2021届高三高考必杀技之结构开放题专练四川省绵阳中学高三2021届高考仿真模拟(一)数学(理)试题四川省绵阳中学2021届高三高考仿真模拟试卷数学(文)试题(一)广东省佛山区大沥高级中学2020-2021学年高三上学期学科素养阶段性调研数学试题2020届山东省济南市高三第一次模拟考试数学试题四川省绵阳市南山中学2022-2023学年高三下学期3月月考数学(文)试题湖北省襄阳四中2021届高三下学期5月高考适应性考试数学试题江苏省南京市第一中学2022-2023学年高三上学期期中数学试题2023年普通高等学校招生统一考试数学模拟预测试题(一)
名校
解题方法
2 . 定义:过椭圆上的一点(不与长轴的端点重合)与椭圆的两个焦点确定的三角形称为椭圆的焦点三角形;已知过椭圆
上一点P(不与长轴的端点重合)的焦点三角形
,且
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a44959d0-896b-471b-98e2-63b465e310c5.png?resizew=175)
(1)求证:焦点三角形
的面积为定值
;
(2)已知椭圆
的一个焦点三角形为
,
;
①若
,求
点的横坐标的范围;
②若
,过点
的直线
与
轴交于点
,且
,记
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa4ae8d7537feb98c7de50302705609.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/29/a44959d0-896b-471b-98e2-63b465e310c5.png?resizew=175)
(1)求证:焦点三角形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d48158ed7791bbea80d88e1cf38831b.png)
(2)已知椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/279cefeb5c389a37a71e5fd3925f5954.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf8a7029669bf1774a24f3ef6273ca88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/faa4ae8d7537feb98c7de50302705609.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d5912296857df3dd11a450963b4e3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/284804b2ed1aa82ded02a38e254b4e38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a372472d5e5637d4f760488bebc20e3e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4179e1ab8705cf19ea7aaf48888843.png)
您最近一年使用:0次
3 . 如图,椭圆
的右焦点为
,过焦点
,斜率为
的直线
交椭圆于
、
两点(异于长轴端点),
是直线
上的动点.
![](https://img.xkw.com/dksih/QBM/2020/7/4/2498208300351488/2499434365116416/STEM/00cea83b99044fdfadc5a725d7ac52ac.png?resizew=202)
(1)若直线
平分线段
,求证:
.
(2)若直线
的斜率
,直线
、
、
的斜率成等差数列,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f7b782201a57a4273747282ee987afa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/707ea658f3a9359f5740d5aab48f7948.png)
![](https://img.xkw.com/dksih/QBM/2020/7/4/2498208300351488/2499434365116416/STEM/00cea83b99044fdfadc5a725d7ac52ac.png?resizew=202)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/874028d1a4daba01fe6e6818293911be.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4f9b8cf2fa888e8d331ea4a446c0ace.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3171b3d11c6f4619e189677345357508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
4 . 已知椭圆
,直线
交椭圆
于
两点,
为坐标原点.
(1)若直线
过椭圆
的右焦点
,求
的面积;
(2)若
,试问椭圆
上是否存在点
,使得四边形
为平行四边形?若存在,求出
的取值范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533b93dd6eb6b474481247736699c76c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.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/1dde8112e8eb968fd042418dd632759e.png)
(1)若直线
![](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/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/839a36f411e39152d2fcf40188d62bc1.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/494296ec6281f15cdaa4e1ada8c690a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
解题方法
5 . 已知点
,
,点
为曲线
上任意一点,且满足![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe53e549f52d6f0b33aa6ac482ae7e3.png)
(1)求曲线
的方程;
(2)曲线
与
轴交于
,
左、右两点,曲线
内的动点
满足
,其中
为坐标原点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.png)
![](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/afe53e549f52d6f0b33aa6ac482ae7e3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68ae369465eb034d89007cd81464d61c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc49ddc2e7dddd18971476817983ac54.png)
您最近一年使用:0次
2020-03-05更新
|
190次组卷
|
2卷引用:四川省绵阳市三台中学实验学校2019-2020学年高二上学期12月月考数学试题
12-13高三上·天津·期末
名校
解题方法
6 . 已知椭圆的一个顶点为
,焦点在
轴上.若右焦点到直线
的距离为3.
(1)求椭圆的方程;
(2)设椭圆与直线
相交于不同的两点
、
,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71885f023172807ad43f2c9a670aa960.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f609ad1adce638dd864449f1c850cf0.png)
(1)求椭圆的方程;
(2)设椭圆与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f556a4584fc8192d526a2bddfc9ccbc.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/3b485b62d004d52fb31d6ed99ccb7669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2016-12-02更新
|
1916次组卷
|
20卷引用:2020届四川省绵阳南山中学高三3月网络考试数学(理)试题
2020届四川省绵阳南山中学高三3月网络考试数学(理)试题(已下线)2012届天津市五区县高三上学期期末考试文科数学试卷(已下线)2012-2013学年福建漳州市芗城中学高二上学期期末考试文科数学试卷(已下线)2014届广东省惠州市高三上学期第二次调研文科数学试卷2016届江西省临川区一中高三10月月考理科数学试卷辽宁省凌源市实验中学、凌源二中2018届高三12月联考数学(理)试卷江西省南昌市第十中学2017-2018学年高二上学期第二次月考数学(理)试题江西省南昌市第十中学2017-2018学年高二上学期第二次月考数学(文)试题【全国百强校】黑龙江省鹤岗市第一中学2018-2019学年高二下学期第二次月考数学(文)试题吉林省吉化第一高级中学校2019-2020学年高二上学期期末数学(理)试题沪教版(上海) 高二第二学期 新高考辅导与训练 第12章 圆锥曲线 阶段训练4重庆市重庆十八中两江实验中学2019-2020学年高二上学期半期(期中)数学试题(已下线)解密12 圆锥曲线中的热点问题(讲义)-【高频考点解密】2021年新高考数学二轮复习讲义+分层训练江西省兴国县第三中学2020-2021学年高二下学期第一次月考数学(理)(兴国班)试题广东省广州中学2021-2022学年高二上学期期中数学试题福建省闽侯县第一中学2021-2022学年高二3月月考数学试题安徽省滁州市定远县育才学校2021-2022学年高二普通班上学期期末文科数学试题安徽省滁州市定远县育才学校2021-2022学年高二(普通班)上学期期末考试数学(文)试题北师大版(2019) 选修第一册 数学奇书 第二章 圆锥曲线 章末整合提升甘肃省兰州市西固区兰州市第六十一中学2023届高三上学期10月月考理科数学试题
11-12高二上·四川绵阳·期中
名校
解题方法
7 . 椭圆
的两个焦点为
、
,
是椭圆上一点,且满
.
(1)求离心率
的取值范围;
(2)当离心率
取得最小值时,点
到椭圆上点的最远距离为
.
①求此时椭圆
的方程;
②设斜率为
的直线
与椭圆
相交于不同两点
、
,
为
的中点,问:
、
两点能否关于过点
、
的直线对称?若能,求出
的取值范围;若不能,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ce0e27d90296a2f2bec69f73d09a9d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/41a99a2034cf37438e8f252a817efa7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fffd834842a7d0457310c4b3f15c42d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d0259c3b233fde0e2b98f05974a069.png)
(1)求离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
(2)当离心率
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9d2d3b514b0720a84d6ad89e9e49f0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9aa82a15632a545ce2cc6dc998899807.png)
①求此时椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
②设斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ff698edaadb3a318d463ce11d53dc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.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/663cdbb62aaec1f5730141c178a6f651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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