1 . 给定椭圆
,称圆心在原点
,半径为
的圆是椭圆
的“伴随圆”.若椭圆
的一个焦点为
,其短轴上的一个端点到
的距离为
.
(1)求椭圆
的方程及其“伴随圆”方程;
(2)若倾斜角为
的直线
与椭圆
只有一个公共点,且与椭圆
的“伴随圆”相交于
两点,求弦
的长;
(3)在椭圆
的“伴随圆”上任取一点
,过点
作两条直线
,使得
与椭圆
都只有一个公共点,且
分别与椭圆的“伴随圆”交于
两点.证明:直线
过原点
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da001dad7941e6c9858637d7b62cec59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eba828e0cec2057bc205fc42d64d370.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ffe8515ff6183c1c7775dc6f94bdb8.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若倾斜角为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1e5fa72f2878b476bc57f0df12d6555.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)在椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f56635924584077092ac3c7dd68837b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.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/1dde8112e8eb968fd042418dd632759e.png)
您最近一年使用:0次
2023-12-08更新
|
437次组卷
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3卷引用:四川省南充市南充高级中学2023-2024学年高二上学期第二次月考数学试题
四川省南充市南充高级中学2023-2024学年高二上学期第二次月考数学试题上海市复旦大学附属中学2023-2024学年高二上学期阶段性学业水平检测2(暨拓展考试6)数学试题(已下线)第2章 圆锥曲线(压轴题专练)-2023-2024学年高二数学单元速记·巧练(沪教版2020选择性必修第一册)
2 . 如图,P为椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
上的动点,过P作椭圆
的切线交圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
于M,N,过M,N作
切线交于Q,则Q的轨迹方程为_______________ ;
的最大值为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef0ac188b55d6377c0ab00a28f3b9296.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6992d4a7cfa2348894f7c991ed6171c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211b9e53e4677ae9e2b20d5f7ce0a4e4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780231ff0af68a65a3d740a2c858b26.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d95f1a8e66ddfb0277c3efb15bf8b7ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39a52e26180930ad5b56a8a45f28a0f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9902b08a6e0aef5eac29c197a356320b.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/24/de5896a5-8ca6-48a2-8ae5-bc88e615bf8e.png?resizew=219)
您最近一年使用:0次
名校
3 . 已知圆
,直线
,点
,点
.给出下列4个结论:
①当
时,直线
与圆
相离;
②若直线
是圆
的一条对称轴,则
;
③若直线
上存在点
,圆
上存在点
,使得
,则
的最大值为
;
④
为圆
上的一动点,若
,则
的最大值为
.
其中所有正确结论的序号是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81c8f7861e8ca0430b88d75cc1285484.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2df29bc4b98cfcc6a3237b5fef779e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1989a364a333cce780a8868436f8c897.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d88965720c6e8c9ffb91105331562e5.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b4d795709b0abcf47bceec2250f2f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
②若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6234d6935565f9ff3ef21f177c542749.png)
③若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cb59543ccf42b37ebce3f67416e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/310f5366592040027f239d7b8a274ba4.png)
④
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39cb59543ccf42b37ebce3f67416e561.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aa52d59e9c95112c75365d420b6d835.png)
其中所有正确结论的序号是
您最近一年使用:0次
2021-01-23更新
|
2560次组卷
|
12卷引用:四川省雅安市天立教育集团2023-2024学年高二上学期期中数学试题
四川省雅安市天立教育集团2023-2024学年高二上学期期中数学试题海南省三亚华侨学校(南新校区)2020-2021学年高二下学期期中考试数学试题(已下线)1.1 命题及其关系提高练-2021-2022学年高二数学同步训练精选新题汇编(人教A版选修2-1)北京市北京理工大学附属中学2021-2022学年高二12月月考数学试题(已下线)高二上学期期中【压轴60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)(已下线)高二上学期第一次月考填空题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)高二上学期期中考试填空题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)重庆市涪陵区部分学校2023-2024学年高二上学期第一次月考数学试题(已下线)上海市华东师范大学第二附属中学2023-2024学年高二上学期10月月考数学试题(已下线)第一次月考检测模拟试卷(原卷版)北京市海淀区2021届高三年级第一学期期末练习数学试题(已下线)考点8-1 直线与圆(文理)
4 . 已知点
到
的距离是点
到
的距离的2倍.
(1)求点
的轨迹方程;
(2)若点
与点
关于点
对称,点
,求
的最大值;
(3)若过
的直线与第二问中
的轨迹交于
,
两点,试问在
轴上是否存在点
,使
恒为定值?若存在,求出点
的坐标和定值;若不存在,请说明理由.
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若点
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78e414c3f13e0e28fe2250bf88e33d5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d436fc4cde0f6490b25bdd6e476332ed.png)
(3)若过
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8649ce18c628d0e03e72cef541f8284f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d405c7e1ed6ddac33126b8c1cb511b6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2020-11-23更新
|
2062次组卷
|
7卷引用:四川省内江市资中县第二中学2020-2021学年高二上11月月考理科试题
名校
解题方法
5 . 已知圆
和点
.
(1)过点
向圆
引切线,求切线的方程;
(2)求以点
为圆心,且被直线
截得的弦长为8的圆
的方程;
(3)设
为(2)中圆
上任意一点,过点
向圆
引切线,切点为
,试探究:平面内是否存在一定点
,使得
为定值?若存在,请求出定点
的坐标,并指出相应的定值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73244638f26130289e00d2ca849b1802.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)求以点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30e24ed3fc5c755b30ebf84772654e1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(3)设
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da2f043e16eacb76ac42474a6f6d399e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
您最近一年使用:0次
2020-07-12更新
|
1774次组卷
|
5卷引用:四川省成都市树德中学2022-2023学年高二上学期10月阶段性测试理科数学试题
名校
解题方法
6 . 已知圆
,直线
.
(1)若直线
与圆
交于不同的两点
,
,当
时,求
的值;
(2)若
,
是直线
上的动点,过
作圆
的两条切线
、
,切点为
、
,探究:直线
是否过定点?若过定点,求出该定点;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd40f44c911918ee3638eb1a24bb1bd9.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/ac51bffb8f476896081027b33f7ec25d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3a2a34b4317deffa40ba34e269c2b81.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9abbd78e9a6840ee5f30381daac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.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/9d78abbad68bbbf12af10cd40ef4c353.png)
您最近一年使用:0次
2020-04-30更新
|
1217次组卷
|
5卷引用:四川省绵阳市三台中学2022-2023学年高二上学期第一次月考数学(理)试题
四川省绵阳市三台中学2022-2023学年高二上学期第一次月考数学(理)试题四川省绵阳市三台中学校2022-2023学年高二上学期第一次月考数学(文)试题安徽省安庆市五校2018-2019学年高二上学期第一次联考数学(理)试题山东省德州市夏津县第一中学2023-2024学年高二上学期10月月考数学试题(已下线)难关必刷03圆的综合问题-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
7 . 抛物线
上一点
到抛物线准线的距离为
,点
关于
轴的对称点为
,
为坐标原点,
的内切圆与
切于点
,点
为内切圆上任意一点,则
的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53ef4efbff159924bdb1f06fc2176f94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e93941f67a248bdbedb285b4e40500.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b8189f7b0ffe4d20bf0fad43b4ed589.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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9卷引用:四川省成都市树德中学2017-2018学年高二12月月考数学(理)试题
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