11-12高三下·福建泉州·阶段练习
1 . 已知圆
:
交
轴于A,B两点,曲线C是以AB为长轴,离心率为
的椭圆,其左焦点为F.若P是圆O上一点,连接PF,过原点O作直线PF的垂线交直线
于点Q.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/5/791f2f33-7b8c-44dd-be50-ceff1589f863.png?resizew=166)
(1)求椭圆C的标准方程;
(2)若点P的坐标为(1,1),求证:直线PQ圆O相切;
(3)试探究:当点P在圆O上运动时(不与A、B重合),直线PQ与圆O是否保持相切的位置关系?若是,请证明;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/5/791f2f33-7b8c-44dd-be50-ceff1589f863.png?resizew=166)
(1)求椭圆C的标准方程;
(2)若点P的坐标为(1,1),求证:直线PQ圆O相切;
(3)试探究:当点P在圆O上运动时(不与A、B重合),直线PQ与圆O是否保持相切的位置关系?若是,请证明;若不是,请说明理由.
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2 . 已知圆
过定点
,圆心
在抛物线
上运动,
为圆
在
轴上截得的弦.
(1)试判断
的长是否随圆心
的运动而变化.并证明你的结论;
(2)当
是
与
的等差中项时,抛物线
的准线与圆
有怎样的位置关系?并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e88523c036b67b0a81238e5b8c4609d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5a9a1832264917c6e730fdce7f599a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(1)试判断
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c388f1f7160d3397610633dfde015fa0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0c19fa4cd646f4d877c3e58cc346651.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/146c403de6b5780cd03e25c775b806c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
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解题方法
3 . 如图,已知定圆
,定直线
,过
的一条动直线
与直线相交于
,与圆
相交于
,
两点,
是
中点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/28f49bdf-3261-4d74-985d-37853a846de9.png?resizew=178)
(1)当
与
垂直时,求证:
过圆心
;
(2)当
时,求直线
的方程;
(3)设
,试问
是否为定值,若为定值,请求出
的值;若不为定值,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0873a0f3245544b4451ec5d2570dbe41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52c434abb1778a406a794336b0de0d62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/23/28f49bdf-3261-4d74-985d-37853a846de9.png?resizew=178)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94b9bfc9045f049b11d4b1c887e6c579.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c53aecada69ab7aa64e233b0a36a916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
您最近一年使用:0次
4 . 已知圆
和直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3528fa597c8f61877f589fae68dac939.png)
(1)求证:不论
取什么值,直线和圆总相交;
(2)求
取何值时,圆被直线截得的弦最短,并求最短弦的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8365d7c7c74eed93f5b9461ce31870f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3528fa597c8f61877f589fae68dac939.png)
(1)求证:不论
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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5 . 已知圆
,直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de811af1f47cbae7e107e73e6be3ad33.png)
(1)证明:不论m为何值,直线l与圆相交;
(2)求直线l与圆
相交弦长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09ebeb7dcd6fcace36d5f66372e20295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de811af1f47cbae7e107e73e6be3ad33.png)
(1)证明:不论m为何值,直线l与圆相交;
(2)求直线l与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
6 . 已知圆
,直线
.
(1)证明直线l总与圆C相交;
(2)当直线l被圆C所截得的弦长为
时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b6177c840f21a6b149ef29aa3f9cfa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21ae92459c4682762669063b425ba963.png)
(1)证明直线l总与圆C相交;
(2)当直线l被圆C所截得的弦长为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
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2021-11-26更新
|
687次组卷
|
6卷引用:云南省下关第一中学2020-2021学年高二上学期段考(一)数学(理)试题
名校
7 . 已知圆C:
,直线l:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804b9282150711812783435bc3c6f080.png)
(1)求证:对
,直线l与圆C总有两个交点;
(2)设直线l与圆C交于点A,B,若
,求直线l的倾斜角;
(3)设直线l与圆C交于点A,
若定点
满足
,求此时直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd580f1e99fc16f8c3cda2bee6b2dc2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/804b9282150711812783435bc3c6f080.png)
(1)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
(2)设直线l与圆C交于点A,B,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed79cde317cee7f73037f66f52f02a50.png)
(3)设直线l与圆C交于点A,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979426d711e6b4ddcefc44f92d8a9062.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/797c488729678e74e0825c2e92b544b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a54dbf1347334c75d15d7e53e078ba.png)
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解题方法
8 . 已知圆C经过两点
,且圆心C在直线
上,直线l的方程为
.
(1)求圆C的方程;
(2)证明:直线l与圆C一定相交;
(3)求直线l被圆C截得的弦长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743a22685aad638418aa50bbab5a00a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e35701dd16dbf6ec916064880b8b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135727cec1ebb852664fd582a600babe.png)
(1)求圆C的方程;
(2)证明:直线l与圆C一定相交;
(3)求直线l被圆C截得的弦长的取值范围.
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2021-08-25更新
|
833次组卷
|
2卷引用:安徽省六安市皖西中学2020-2021学年高二上学期期中文科数学试题
2022高三·全国·专题练习
9 . 已知直线l:2mx-y-8m-3=0和圆C:x2+y2-6x+12y+20=0.
(1)m∈R时,证明l与C总相交;
(2)m取何值时,l被C截得的弦长最短?求此弦长.
(1)m∈R时,证明l与C总相交;
(2)m取何值时,l被C截得的弦长最短?求此弦长.
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2021-10-08更新
|
1060次组卷
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8卷引用:浙江省丽水外国语实验学校2020-2021学年高二上学期第一次段考数学试题
浙江省丽水外国语实验学校2020-2021学年高二上学期第一次段考数学试题(已下线)专题12 直线和圆的方程-备战2022年高考数学一轮复习核心知识全覆盖(新高考地区专用)江西省宜春市上高二中2021-2022学年高二上学期10月月考数学(理)试题河南省焦作市温县第一高级中学2021-2022学年高二上学期10月月考数学(理)试题江西省宜春市上高二中2021-2022学年高二上学期第一次月考数学(理)试题上海市嘉定区第二中学2021-2022学年高二上学期期末数学试题(已下线)第十四课时 课中 第二章 章末复习1.2.3直线与圆的位置关系(习题) -2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册
11-12高二·浙江舟山·阶段练习
名校
10 . 已知圆
,直线
.
(1)求证:对
,直线
与圆
总有两个不同交点;
(2)设
与圆
交与不同两点
,求弦
的中点
的轨迹方程;
(3)若直线过点
,且
点分弦
为
,求此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c406915922045153a67d269f41ac4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3445947fa34dd409a1354786e6c4a579.png)
(1)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/ac047e91852b91af639feec23a9598b2.png)
(3)若直线过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ad08989b99ce8a2d9ac6311cffce124.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2021-07-22更新
|
864次组卷
|
9卷引用:2011-2012学年浙江省嵊泗中学高二第一次月考数学试卷(7-8班)
(已下线)2011-2012学年浙江省嵊泗中学高二第一次月考数学试卷(7-8班)重庆市重庆复旦中学2020-2021学年高二上学期第一次段考数学试题浙江省台州市书生中学2020-2021学年高二下学期期中模拟数学试题(已下线)第二章 (综合培优)直线和圆的方程 B卷-【双基双测】2021-2022学年高二数学同步单元AB卷(浙江专用)(人教A版2019选择性必修第一册)(已下线)试卷07(第1章-2.3圆与圆的位置关系)-2021-2022学年高二数学易错题、精典题滚动训练(苏教版2019选择性必修第一册)(已下线)专题09 直线与圆、圆与圆的位置关系 - 2021--2022高二上学期数学新教材配套提升训练(人教A版2019选择性必修第一册)(已下线)2.5直线与圆、圆与圆的位置关系(专题强化卷)-2021-2022学年高二数学课堂精选(人教A版2019选择性必修第一册)(已下线)专题2.3 圆与方程 章末检测3(难)-【满分计划】2021-2022学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)河北省献县求是学校2022-2023学年高二上学期9月月考数学试题