1 . 已知圆C经过
,
两点和坐标原点O.
(1)求圆C的方程;
(2)垂直于直线
的直线
与圆C相交于M,N两点,且
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e95e84f5c91c910aaafc5e74dbfbdf59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29610a3415c1e795d35979a5a9ff69f3.png)
(1)求圆C的方程;
(2)垂直于直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f1a686b80b8f109a929f58c2de7201d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14a85d5d71e238da9f4e499faec0f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-22更新
|
202次组卷
|
2卷引用:天津市部分区2023-2024学年高二上学期期末练习数学试题
名校
解题方法
2 . 已知圆
的圆心在直线
上且与
轴相切,圆
被直线
截得的弦长为4.
(1)求圆
的标准方程;
(2)从圆
外一点
向圆
引一条切线,切点为
,
为坐标原点,且
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08b9f0b9e53a83e68f5fec944f343119.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)从圆
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e0cac807d10c3dc2f00f29d1687f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d341082cc54b1cb7a790af9ec4a365d.png)
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2024-01-20更新
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180次组卷
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2卷引用:广东省深圳市光明区2023-2024学年高二上学期期末学业水平调研测试数学试题
3 . 已知直线l的倾斜角为
,且过点
,
(1)求直线l的直线方程;
(2)若以原点为圆心的圆C恰好与直线l相切,求圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4c5016bd1fc6582078299b9cf8b392.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db7cb5891cc7c859eda6e73c17a99a63.png)
(1)求直线l的直线方程;
(2)若以原点为圆心的圆C恰好与直线l相切,求圆C的方程.
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名校
4 . 已知圆的圆心为直线
与直线
的交点,且圆
的半径为
.
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](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/e76cb7c345f355208c133c1adf592ad8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9348fd78ebbdafe9edbc3073997a16e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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名校
解题方法
5 . 圆
与
轴的交点分别为
,
且与
和
都相切.
(1)求圆
的方程;
(2)圆
上是否存在点
满足
?若存在,求出满足条件的所有点
的坐标;若不存在,请说明理由.
![](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/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fbdef5d0c05acbf63fa72fa85c5bb45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a834980769b54d11360e48ecaf98c48d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7d24b36cde215a67af97c5f07dd226.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)圆
![](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/0f3ec999575add4fded6465cc2944683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2024-01-13更新
|
595次组卷
|
2卷引用:辽宁省五校联考2023-2024学年高二上学期1月期末数学试题
名校
6 . 如图,在宽为14的路边安装路灯,灯柱
高为8,灯杆
是半径为
的圆
的一段劣弧.路灯采用锥形灯罩,灯罩顶
到路面的距离为10,到灯柱
所在直线的距离为2.设
为灯罩轴线与路面的交点,圆心
在线段
上.以
为原点,以
所在直线为
轴建立平面直角坐标系.
(1)当点
恰好为路面中点时,求此时圆
的方程;
(2)记圆心
在路面上的射影为
,且
在线段
上,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.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/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/26/5c6ac040-433a-4682-9a32-4e60ec958eee.png?resizew=252)
(1)当点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记圆心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c018b37259f3ead2ab2d94bd744f44d.png)
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2024-01-13更新
|
270次组卷
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3卷引用:上海市进才中学2023-2024学年高二上学期1月期末考试数学试题
7 . 已知![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b20b5d63f5ff183064fc601b404e070.png)
(1)过点A作直线
,交直线
和直线
于
两点,A为线段
的中点.求直线
的方程;
(2)若圆
的圆心在直线
上,圆
经过点
.求圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b20b5d63f5ff183064fc601b404e070.png)
(1)过点A作直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6cccbf00db665298ac43c169d9df921.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dab13543ac1b7aa9fe583f3b229241b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a373959bb9026f8a09845c0b828bf82.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b2caf6048aa0807d8ba591963ff6e2.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/c5db41a1f31d6baee7c69990811edb9f.png)
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8 . ①经过点
;②与x轴相切,半径为2;③被直线
平分.从这三个条件中任选一个,补充在下面问题中,并完成解答.(注:如果选择多个条件分别解答,按第一个解答计分)
已知圆M经过点
,点
, .
(1)求圆M的方程;
(2)设
,P是圆上任意一点,当
取得最大值时,求过点P的圆M的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d3b76fed893ad17bc60ee4cbe4ab524.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/107babba45f110012183dc4dc54490f7.png)
已知圆M经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1dab74e16403e8131f9f5b2a74f3a84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4af0146cc33172061d379549fe9e291.png)
(1)求圆M的方程;
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71fb572a6f07dcade5332bea766020f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f3f2cf845cdf57834ed71b61fc426b4.png)
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2024-01-11更新
|
254次组卷
|
3卷引用:江苏省2023-2024学年高二上学期期末迎考数学试题(B卷)
名校
解题方法
9 . 已知圆心C在直线
上,圆C过点
,
.
(1)求圆C的标准方程;
(2)已知点
,求过点M的圆C的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e894db81047f81df006964a290c039cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193c0af60bce74c8f575dc8dc3ea0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a0066672fdf6e591b842847e5a6c7c.png)
(1)求圆C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
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10 . 在平面直角坐标系
中,圆
的半径为
,其圆心在射线
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e058ef2a64b0d5a5a5ce4c6c8a028aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求圆
的标准方程;
(2)若直线
过点
, 且与圆
相切,求直线
的方程;
(3)自点
发出的光线
射到
轴上,被
轴反射,其反射光线所在的直线与圆
相切,求光线
所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfb764b285362ee742b6dc613a1460a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e058ef2a64b0d5a5a5ce4c6c8a028aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)自点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c058a8ba318315dde9c5a0392944b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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