1 . 已知圆
,直线
.
(1)求证:直线l恒过定点;
(2)直线l被圆C截得的弦长何时最长、何时最短?并求截得的弦长最短时a的值以及最短弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/742a56e08b5809e6d605305fa6f379de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5732777f768c346dfe195e3511b9dc60.png)
(1)求证:直线l恒过定点;
(2)直线l被圆C截得的弦长何时最长、何时最短?并求截得的弦长最短时a的值以及最短弦长.
您最近一年使用:0次
2023-12-15更新
|
288次组卷
|
2卷引用:湖南省长沙市长沙县第二中学2023-2024学年高二上学期期中数学试题
解题方法
2 . 已知圆
的圆心为
(
且
),
,圆
与
轴、
轴分别交于
,
两点(与坐标原点
不重合),且线段
为圆
的一条直径.
(1)求证:
的面积为定值;
(2)若直线
经过圆
的圆心,求圆
的方程;
(3)在(2)的条件下,设
是直线
上的一个动点,过点
作圆
的切线
,
,切点为
,
,求线段
长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3b5fe7ff4823684bcbd303eb74833a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca27cc54ca0332245f5167488daa3408.png)
![](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/d053b14c8588eee2acbbe44fc37a6886.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)在(2)的条件下,设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/045cf6c42c53f44921c55a01fc4cdd8c.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/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35d58f9019097bd05037aefd5c322916.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/803a617fb53e67edbc2955cb629c329b.png)
您最近一年使用:0次
解题方法
3 . 已知圆
的圆心为
,半径为3,
是过点
的直线.
(1)求圆
的方程,并判断点
是否在圆上,证明你的结论;
(2)若圆
被直线
截得的弦长为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/879a4007beef22e009248112d664f7c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5c10f14aae6fb21e047ecb39cdf40c0.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
4 . 已知圆
,直线
.
(1)求证:直线
恒过定点.
(2)直线
被圆
截得的弦长最短时
的值以及最短弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be1cd21b824fcf58c75911fb165306d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f62622393abcb2f164c14c46d7946226.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2024-01-26更新
|
288次组卷
|
2卷引用:四川省成都市第三十六中学2023-2024学年高二上学期期中考试数学试题
5 . 如图,过点
的直线与圆
:
相交于两点
,过点
且与
垂直的直线与圆
的另一交点为
.
(1)记点
关于
轴的对称点为
(异于点
),求证:直线
恒过定点;
(2)求四边形
面积
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33a62c9695f5a1691c5fe8724fa764b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08227ca941898eb34941f446ca8b1de8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49179dbfbc8e207aa92fd72060fba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/10/19/1d4050d9-81a6-4de0-954f-31ba361537ba.png?resizew=176)
(1)记点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274cf35acb4a1748d15c39d15a9bea7b.png)
(2)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c593ebdb2f1934a0cb56f8c44f454f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2023-09-30更新
|
704次组卷
|
5卷引用:福建省宁德市2022-2023学年高二上学期区域性学业质量监测(期中)数学试题
福建省宁德市2022-2023学年高二上学期区域性学业质量监测(期中)数学试题福建省福州格致中学2023-2024学年高二上学期期中考试数学试题江西省宜春市丰城中学2023-2024学年高一创新班上学期期中数学试题(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)(已下线)专题17 直线与圆的位置关系9种常见考法归类- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教B版2019选择性必修第一册)
6 . 已知圆
:
,直线
:
.
(1)求证:直线
恒过定点;
(2)求直线
被圆
截得的弦最短时
的值以及最短弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85bc1c5ec31cf3b832d7f76a7edbefd8.png)
(1)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求直线
![](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/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
名校
解题方法
7 . 已知圆
.
(1)证明:圆
过定点.
(2)当
时,求直线
被圆
截得的弦长.
(3)当
时,若直线
与圆
交于
两点,且
,其中
为坐标原点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4317a470672a5a775ec09c06d7ac96cf.png)
(1)证明:圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f2f2d7c81cb44416bcdf59419637682.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb0d6d0cfe389abca252332223b5da17.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/331c27b493b12fc43837085e9bcfd83d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
您最近一年使用:0次
2023-10-05更新
|
951次组卷
|
3卷引用:期中考前必刷卷01(范围:第1章~3.2 基础卷)-2023-2024学年高二数学上学期期中考点大串讲(苏教版2019选择性必修第一册)
(已下线)期中考前必刷卷01(范围:第1章~3.2 基础卷)-2023-2024学年高二数学上学期期中考点大串讲(苏教版2019选择性必修第一册)河北省邢台市四校质检联盟2023-2024学年高二上学期第一次月考数学试题河北省邢台市河北南宫中学2023-2024学年高二上学期第一次月考数学试题
8 . 已知圆
,直线
.
(1)求证:直线l恒过定点;
(2)当
时,求直线l被圆C截得的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c1a0d6d9bd895f00222199cf09d9073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be540f923e9e9252f5ff681de79f2050.png)
(1)求证:直线l恒过定点;
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd876a2ed79c64bacc3e64b8ee92735e.png)
您最近一年使用:0次
2023-08-22更新
|
828次组卷
|
12卷引用:江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题
江西省吉安市双校联盟2022-2023学年高二下学期期中考试数学试题新疆维吾尔自治区喀什市第十中学2023-2024学年高二上学期期中考试数学试题甘肃省临夏回族自治州广河中学2022-2023学年高二上学期期末数学试题宁夏回族自治区银川市第二中学2023-2024学年高二上学期第一次月考数学试题山东省青岛市青岛第二中学2021-2022学年高二上学期10月月考数学试题江苏省连云港华杰高级中学2023-2024学年高二上学期9月阶段检测数学试题河南省周口市郸城县第一高级中学2023-2024学年高二上学期第一次月考数学试题(已下线)第二章 直线与圆的方程(知识归纳+题型突破)-2023-2024学年高二数学单元速记·巧练(人教A版2019选择性必修第一册)(已下线)第03讲:直线与方程 (必刷8大考题+9大题型)-2023-2024学年高二数学上学期《考点·题型·难点》期末高效复习(人教A版2019)(已下线)第02讲 2.4圆的方程+2.5直线与圆,圆与圆的位置关系(2)湖南省岳阳市平江县2023-2024学年高二上学期期末教学质量监测数学试题(已下线)高二上学期期末考点大通关真题精选100题(2)
名校
解题方法
9 . 已知圆
,直线
,直线l与圆C相交于P,Q两点,M为线段PQ的中点.
(1)若
﹐求直线l的方程:
(2)若直线l与直线
交于点N,直线l过定点A,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1b8df651dbb5ef75a6172c67f541c0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764ab1262baa09cd62fb6ddba39df2ec.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47fd70e8ec8aa4aada7f05e2d4778d32.png)
(2)若直线l与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ec4bce5f4f7d042e16c0ce4bd1428b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdc7bdc6448ef9a13c59fdce1b9bb57.png)
您最近一年使用:0次
2023-02-14更新
|
348次组卷
|
5卷引用:专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)
(已下线)专题05 直线与圆综合大题18种题型归类-【巅峰课堂】2023-2024学年高二数学上学期期中期末复习讲练测(人教A版2019选择性必修第一册)甘肃省庆阳市宁县第二中学2022-2023学年高二上学期期末数学试题甘肃省天水市第一中学2022-2023学年高二上学期1月期末考试数学试题甘肃省武威市第八中学2023-2024学年高二上学期期末数学试题(已下线)通关练11 圆的方程大题10考点精练(47题)- 【考点通关】2023-2024学年高二数学高频考点与解题策略(人教A版2019选择性必修第一册)
10 . 已知直线
和圆
.
(1)证明:圆C与直线l恒相交;
(2)求出直线l被圆C截得的弦长的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a7171cb15949949f40809627cf741b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9e08fa81cc6f1097a20f8e97766f24.png)
(1)证明:圆C与直线l恒相交;
(2)求出直线l被圆C截得的弦长的最小值.
您最近一年使用:0次
2023-03-23更新
|
509次组卷
|
3卷引用:浙江省金华市曙光学校2023-2024学年高二上学期期中数学试题