名校
1 . 已知圆
.
(1)若过点
向圆C作切线l,求切线l的方程;
(2)若Q为直线
上的动点,
是圆
上的动点,定点
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/997765e2c34222992649cb946218df55.png)
(1)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a436db19eb954d31075d5398f1b92ecd.png)
(2)若Q为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b2a29cc492d67e2a8a46631f21245c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf1bfd30237dce059d0107506d7be9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/350a38070bdc27207946be17d5f70223.png)
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2024高三·全国·专题练习
2 . 已知圆O1:x2+y2-8x-8
y+48=0,圆O2过点A(0,-4).
(1)若圆O2与圆O1相切于点B(2
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
(2)若圆O2过点C(4,0),圆O1,O2相交于点M,N,且两圆在点M处的切线互相垂直,求直线MN的方程.
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解题方法
3 . 已知圆
:
.
(1)若直线
过定点
,且与圆
相切,求
的方程;
(2)若圆
的半径为
,圆心在直线
:
上,且与圆
外切,求圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4d08158fd61e70c9e46e81c793b96fe.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca979687ffb2214e747525635a6912c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dcaada7649455fbebcdbdbb9a94e6a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
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4 . 已知圆
,点
是圆
上一点,点
为直线
上的动点,过点
作圆
的切线,切点为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
(1)求过点
的圆
的切线方程;
(2)以
为圆心的圆交圆
于
两点,问直线
是否恒过一定点?若过定点求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b6b7d640854325525ea392168574f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c64fe18cf7bb6e26eb1e4409b441965b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38b6b7d640854325525ea392168574f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86e203b7c9a6600e0272c58a23733490.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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解题方法
5 . 已知圆
经过点
,
,
.
(1)求圆
的方程;
(2)过点
作直线
与圆
相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c6ff81aedbefa935da289dc632e78eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76d03fa28c117649b0fdfe17eed7b583.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a77cb0a28d72b7e7eacc877e97bc7ff7.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a436db19eb954d31075d5398f1b92ecd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
6 . 已知圆
的方程为
,点
的坐标为
.
(1)求过点
且与圆
相切的直线
的方程;
(2)直线
过点
,且与圆
交于
两点,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce7aa72cea164858361429853492d30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8156a557d9b963a77dfd88178789ac7.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/84cef568cfe2fc12a4dec11533ada274.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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解题方法
7 . 如图,在平面直角坐标系
中,点
,直线
,设圆C的半径为1,圆心在l上.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
上,过点A作圆C的切线,求切线的方程;
(2)若圆C上存在点M,使
,求圆心C的横坐标a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc878a5fd7b508cf817cbb65d3940547.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6db0a1cbf7b0ed76c443b953af8734d0.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/2/29/5426adc8-1854-4d34-b385-3a24824b222a.png?resizew=147)
(1)若圆心C也在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b8c1212804e6d784756d48083d166e8.png)
(2)若圆C上存在点M,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a464b0c729f294287d3d89119a585293.png)
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名校
解题方法
8 . 已知点
,圆
.
(1)求过点
的圆的切线方程;
(2)若直线
与圆相交与A,B两点,且弦
的长为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/706e0350fd1c36a4e3c66868a8218a7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331a133d2fff3d6e402f25143167fba9.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6229fbdb2c3609beb75bf79952bcdc1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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名校
解题方法
9 . 已知点
,点
在圆
上运动.
(1)求过点
且与圆
相切的直线方程;
(2)已知
,求
的最值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ce7be37ff9418a9c95d5dc54814ebd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99855445965a01665158620054410fe7.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3eba3f26953efa2ea3b55c6bc04964bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aed9a3976b506be220a26873931651b2.png)
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解题方法
10 . 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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