1 . 已知圆
经过
和
两点,且圆心在直线
上.
(1)求圆
的方程;
(2)若一条光线从点
射出,经直线
反射后,恰好与圆
相切,求反射后光线所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241ce9bd28046ce9b90f43b391132884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/89470068f2cfa4229e471c50065c63ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9eaa224254a49065d213ca3a2f75f0db.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若一条光线从点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ec95c668d7863e45d15d1d62307d415.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09324568f2f3995b2f932e66ee5926ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
2 . 已知圆
.
(1)直线
过点
,且与圆
相切,求直线
的方程;
(2)设直线
与圆
相交于
,
两点,点
为圆
上的一动点,求
的面积S的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7238e5ddb32508cf9ce9b0bb9e114083.png)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9381f1ad112d9a635f76a1aa061a3de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/91b51d3992644d37dc71c9b5a97d515c.png)
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解题方法
3 . 已知圆
外有一点
,过点P作直线l.
(1)当直线l过圆心C时,求直线l的方程;
(2)当直线l与圆C相切时,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/db078760974c0b1d214dcf4924dacb40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80ad4f92ee1f742cd54a8f16756cbd65.png)
(1)当直线l过圆心C时,求直线l的方程;
(2)当直线l与圆C相切时,求直线l的方程.
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4 . 已知圆
,A是圆C上一动点,点
,M为线段
的中点.
(1)求动点M的轨迹方程;
(2)记M的轨迹为曲线E,过点
的点线l与曲线E有且只有一个交点,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bae743ec527b0075bf098d435a138bf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d03fa28c117649b0fdfe17eed7b583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(1)求动点M的轨迹方程;
(2)记M的轨迹为曲线E,过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfaaac9b7ed3db514f5bad049a23b389.png)
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2023-11-10更新
|
393次组卷
|
2卷引用:重庆市南开中学校2023-2024学年高二上学期期中数学试题
名校
5 . 在平面直角坐标系中,已知直线l经过直线
和
的交点P.
(1)若直线l与直线
平行,求直线l的方程;
(2)若直线l与圆
相切,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae122aee6f0eafcc559a73b3e905fc78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb343cfed5f78a4a24f750415abef43e.png)
(1)若直线l与直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d937d4bf2152bb2745d92361884b75a3.png)
(2)若直线l与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f6a96a5c814ff54e5bfa9243883cf8f.png)
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2023-11-09更新
|
277次组卷
|
2卷引用:江苏省苏州中学2023-2024学年高二上学期期中数学试题
名校
解题方法
6 . 已知点
,
,圆
的半径为1.
(1)若圆
的圆心坐标为
,过点
作圆
的切线,求此切线的方程;
(2)若圆
的圆心
在直线
:
上,且圆
上存在点
,使
,
为坐标原点,求圆
圆心的横坐标
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca8316866d8f61424c8ef98d5882ba8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27149c9ff20937492950f42084caa019.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62e6975f591732cb9758fe76a2e12557.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](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/9e6e15daf7b14dbff32c390f4984dcfb.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/25782bc6046a2c90189bd78ec6f68ff8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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解题方法
7 . 阿波罗尼斯(约公元前262-190年)证明过这样一个命题:平面内到两定点距离之比为常数
(
且
)的点的轨迹是圆,后人将这个圆称为阿氏圆.已知动点
到点
与点
的距离之比为2,记动点
的轨迹为曲线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
的方程;
(2)过点
作曲线
的切线
,求曲线
关于直线
对称的曲线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bb8775b827a649b07b6c2f8c3ea284.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90f8358fa8cd9bc8c99ea48d9ae1a2.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
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8 . 已知圆
,直线
.
(1)求圆
关于直线
对称的圆的标准方程;
(2)
是直线
上的动点,过
点作圆
的切线
,切点为
,求切线长
最短时切线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4da87c834af5c1287120382922abf82b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fa0667ad7e7060032787706750f409e.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
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9 . 已知圆
经过坐标原点
和点
,且圆心在
轴上.
(1)求圆
的标准方程;
(2)设直线
经过点
,且
与圆
相交所得弦长为
,求直线
的一般式方程;
(3)求过点
与圆
相切的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b86022205a7487439dd8d0897cd3bf19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.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/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d00d5d8cc31aaca7fc2eafb99eac7629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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10 . 已知点
在圆
上运动,点
为线段
的中点,设点
的轨迹为曲线
,
(1)求曲线
的轨迹方程.
(2)过点
作曲线
的切线
,求切线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c0e24903ffe9060ed494b9e369e477.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9671ddb5fe9a70824a296c17dcb6e254.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8543a9925dffcc9c0c0e13cff19732a2.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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