1 . 已知点
为坐标原点,
的直径为2,点
,点
是
:
上的动点,记线段
的中点
的轨迹为Γ.
(1)求Γ的方程;
(2)判断Γ与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d00483a05dd88fbd59cd2c95dbaf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求Γ的方程;
(2)判断Γ与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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名校
2 . 已知点
,
,
的方程为
,点
是
上的动点.
(1)求
面积的取值范围;
(2)是否存在点
,使得
?若存在,求出满足条件的点
的个数;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a23e87d16c32b5aa4357f481b5808a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a924404906373977a09c02943427037f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2205cffebf8c4d5f81d15ed7b85c8936.png)
(2)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab34ce6cee0673ab0d37b660d57bc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2023-10-17更新
|
181次组卷
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3卷引用:福建省永安市第九中学2023-2024学年高二上学期第一次月考测试数学试题
名校
解题方法
3 . 古希腊著名数学家阿波罗尼斯发现:“平面内到两个定点
的距离之比为定值
的点的轨迹是圆”.后来,人们将这个圆以他的名字命名,称为阿波罗尼斯圆,简称阿氏圆.在平面直角坐标系
中,
,
,点
满足
.
(1)求
的轨迹方程;
(2)设圆
是以
为直径的圆,求证圆
与圆
相交,并求公共弦所在的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08f5d6f91366da27e9b96452bb04977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/316ba5cbb31299d683ac6c7dd795db85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df5d30e4268a4b86a4e098e8cb57da3.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)设圆
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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4 . 如图,某海面上有O、A、B三个小岛(面积大小忽略不计),A岛在O岛的北偏东45°方向
处,B岛在O岛的正东方向20km处.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/ee26880f-9128-4371-8641-e0a3e588f331.png?resizew=177)
(1)以O为坐标原点,O的正东方向为x轴正方向,1km为单位长度,建立平面直角坐标系,写出A、B的坐标,并求A、B两岛之间的距离;
(2)已知在经过O、A、B三个点的圆形区域内有未知暗礁,现有一船在O岛的南偏西30°方向距O岛20km处,正沿着北偏东60°行驶,若不改变方向,试问该船有没有触礁的危险?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4756a61453b03c44503b6fc78870444.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/4/9/ee26880f-9128-4371-8641-e0a3e588f331.png?resizew=177)
(1)以O为坐标原点,O的正东方向为x轴正方向,1km为单位长度,建立平面直角坐标系,写出A、B的坐标,并求A、B两岛之间的距离;
(2)已知在经过O、A、B三个点的圆形区域内有未知暗礁,现有一船在O岛的南偏西30°方向距O岛20km处,正沿着北偏东60°行驶,若不改变方向,试问该船有没有触礁的危险?
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2023-04-07更新
|
161次组卷
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4卷引用:福建省泉州第一中学2021-2022学年高二上学期期中考试数学试题
5 . 在平面直角坐标系
中,已知圆
过点
,且圆心
在直线
上;圆
:
.
(1)求圆
的标准方程,并判断圆
与圆
的位置关系;
(2)直线
上是否存在点
,使得过点
分别作圆
与圆
的切线,切点分别为
(不重合),满足
,若存在,求出点
的坐标,若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6917df35ab960d5958af89095219434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aefcbc03a5c916ebb20f891a0fe7e0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23ac2e107fc8c5a15f19ce3a140c7ec2.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.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/1e05a08553ae90b96af99544a0e45008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/916d55867b745e841537754f34b440c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2021-11-21更新
|
765次组卷
|
7卷引用:福建省莆田华侨中学2022-2023学年高二上学期期中考试数学试题
福建省莆田华侨中学2022-2023学年高二上学期期中考试数学试题广西钦州市2020-2021学年高一下学期期末数学试题(已下线)第17讲 圆与圆的位置关系-【帮课堂】(已下线)专题2.17 直线和圆的方程大题专项训练(30道)-2021-2022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)湘教版(2019) 选修第一册 突围者 第2章 第七节 用坐标方法解决几何问题湘教版(2019) 选修第一册 突围者 第2章 第七节 用坐标方法解决几何问题2023版 湘教版(2019) 选修第一册 过关斩将 第2章 平面解析几何初步
名校
解题方法
6 . 已知圆
与圆
关于直线
对称,且点
,
在圆
上,
(1)判断圆
与圆
的位置关系;
(2)设
为圆
上任意一点,
.
,
与
不共线,
为
的平分线,且交
于
,求证
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7ee6bc05c47955e29e0dd16bf16097e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a81fbd18e40aeb400e7191227de47bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f39cabc276425e878294dcbb30c5cf37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)判断圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(2)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/35af8a223d55ef90910a778c932ea1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d9ce9420cd614b74030d2f73629f7de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d956b09c004ddf8bdf6669a8182e80ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8e287cd7e75c3199af6f935492c947a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4505508b3e36db64a207dcdaf8eb22dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c965f16192e57a8079a40a0304ef339b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1269ea1057c555e256a8ea4a717e0f0.png)
您最近一年使用:0次
2020-10-29更新
|
323次组卷
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4卷引用:福建省厦门市思明区松柏中学2020-2021学年高二(10月份)学情诊断数学试题
福建省厦门市思明区松柏中学2020-2021学年高二(10月份)学情诊断数学试题(已下线)对点练52 圆与圆的位置关系-2020-2021年新高考高中数学一轮复习对点练安徽省马鞍山市第二中学郑蒲港分校2020-2021学年高二下学期入学摸底测试文科数学试题(已下线)高二数学下学期开学摸底卷(测试范围:选修一+选修二)-2021-2022学年高二数学下学期考试满分全攻略(人教A版2019选修第二册+第三册)
解题方法
7 . 如图所示,已知直线
,圆
的圆心为
,且经过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3d95739a-049c-4df9-b5fa-6d536ff9daa6.png?resizew=135)
(1)求圆
的方程;
(2)若圆
与圆
关于直线
对称,点
分别为圆
,
上任意一点,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c037b199f33cbed1efcffdd2376d8c10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88c3a2f5b0702ea9fbb9dc8904579737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab47bf43b2c5d6395129b80ddfbb1b24.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/24/3d95739a-049c-4df9-b5fa-6d536ff9daa6.png?resizew=135)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbdb21011ea821b91d539cb763aac649.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76a0abdf3eea0772418890031971fb56.png)
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