1 . 已知圆
经过三点
,
,
.
(1)求圆
的方程;
(2)过
的直线
与圆
交于另一点
,且
为等腰直角三角形,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32366143230ca122894a4bada7c7b96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4f68f688a0af020ed2aa105a1bcdb52.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4b13964019381c4cd9de05f95c4261b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
2 . 已知
,圆
为
的外接圆.
(1)求圆
的方程;
(2)若过点
的直线
被
截得的弦长为
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e8ca83e2a3829f46ca8d233a036ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8f9648c81481bb487a43f95c04d991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
3 . 已知圆
经过三点
.
(1)求圆
的方程;
(2)求过点
且与圆
相切的直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f971512343d79708a55d63ca8b07395.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
4 . 在△OAB中,O是坐标原点,
,
.
(1)求AB边上的高所在直线的方程;
(2)求△OAB的外接圆方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bdfc750fe0ace842a461e89f2b7b290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
(1)求AB边上的高所在直线的方程;
(2)求△OAB的外接圆方程
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5 . 如图,四边形
是一块长方形绿地,
是一条直路,交
于点
,交
于点
,且
.现在该绿地上建一个标志性建筑物,使建筑物的中心到
三个点的距离相等.以点
为坐标原点,直线
分别为
,
轴建立如图所示的直角坐标系.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/c42ec9a0-7c79-46fd-9935-534367339523.png?resizew=140)
(1)求出建筑物的中心
的坐标;
(2)由建筑物的中心到直路
要开通一条路,已知路的造价为150万元
,求开通的这条路的最低造价.
(附:参考数据
.)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b915251edf729c1e3d86edc68c05cc3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2dca049735b45fb9b2533c68605eddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554e31ce2d5c31a429a2fceb44156840.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37c67354b5eaa433b3114be6f559b0d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b337a09a149e222af0d636d3d63edb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/13/c42ec9a0-7c79-46fd-9935-534367339523.png?resizew=140)
(1)求出建筑物的中心
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)由建筑物的中心到直路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08cce6cac0fdd4b1a434af8bcaec8fef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a98024ce2e23a5e81b2bcdd7c96ccef9.png)
(附:参考数据
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bb8e063747281398c27620b4d25bc0c.png)
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6 . 已知圆
:
与圆
:
相交于A,B两点,则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376bc360486059a9674a964d031e9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28da6766230aeb546a2588daf93958ff.png)
A.两圆的相交弦所在直线方程为![]() |
B.两圆的公共弦长为![]() |
C.经过A,B两点,且过原点的圆的方程为![]() |
D.P为![]() ![]() ![]() |
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名校
解题方法
7 . 已知圆
与直线
交于A,B两点,则经过点A,B,
的圆的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f3b4416a186069ad6dbe9d9c1ed76e8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51775ad7d2e925dfbc4c9fa3ba4ee0f1.png)
您最近一年使用:0次
2024-02-04更新
|
1612次组卷
|
4卷引用:浙江省温州市2024届高三上学期期末考试数学试题
解题方法
8 . 已知圆C经过点
和点
,且圆心在y轴上,则圆C的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/455ba3d3e46977fcbe5b71f8bb9df4be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知直线
,直线l过点
且与
垂直.
(1)求直线l的方程;
(2)设l分别与
交于点A,B,O为坐标原点,求过三点A,B,O的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/091f6b259b5838d134dc98d02cd53766.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e47de76d65bca1038670bd9e98d6290.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(1)求直线l的方程;
(2)设l分别与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
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10 . 已知直线
过点
且与直线
平行,圆
经过点
.
(1)求直线
的方程;
(2)求圆
的标准方程;
(3)点
是圆
上的动点,求点
到直线
的距离最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b20558865ec54ceea2a53db238695534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/550e145323901c748a4d587f62f80970.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72191ead1d8ec146200378d750d223a4.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)点
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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