名校
解题方法
1 . 已知圆C:
.
(1)求过点
且与圆C相切的直线方程;
(2)求圆心在直线
上,并且经过圆C与圆Q:
的交点的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85300de5f398c86e24b52e0a2298f6a9.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36d02c9e0fecab6c546da6473d32912.png)
(2)求圆心在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331a133d2fff3d6e402f25143167fba9.png)
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2024-02-03更新
|
87次组卷
|
2卷引用:云南省玉溪第一中学2023-2024学年高二上学期期中考试数学试卷
2 . 已知圆
经过
两点,且圆心
在
轴上,一条光线从点
射出,经
轴反射后,与圆
相切.
(1)求圆
的方程;
(2)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/d21b13ceffd3a962d423e470925f9b94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad41d4cfe732c1f2a903c4091c784dfb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求反射后光线所在直线的方程.
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名校
解题方法
3 . 已知⊙M:
,直线l:
,点P在直线l上,过点P作⊙M的切线PA,PB,切点分别为A,B.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/95113a65-89d8-4265-9b50-25cab1bbcc61.png?resizew=160)
(1)若
,试求点P的坐标;
(2)直线AB是否过定点,若过定点,求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7253d9e65b4e64aa4ca83b2302e0c96d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/31/95113a65-89d8-4265-9b50-25cab1bbcc61.png?resizew=160)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b15b82151bff7cc0238d2034a6129f0.png)
(2)直线AB是否过定点,若过定点,求出定点坐标.
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名校
4 . 已知半径为1的圆经过点
,过点
向圆作切线,则切线长的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f1e95fb519f59c46f40e4ab44660073.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/accf35598ee054f1bf8b6584641d6d85.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-31更新
|
227次组卷
|
2卷引用:北京市平谷区2023-2024学年高二上学期期末教学质量监控数学试卷
5 . 已知点
是圆
上的动点,则下面说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7775aa57ca0e62216f3039ed88dceed0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e93e12b8b1c6c7ec759748229f2c475a.png)
A.圆的半径为2 | B.![]() ![]() |
C.![]() ![]() | D.![]() |
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6 . 已知圆
,点
.
(1)求圆C的圆心坐标及半径;
(2)求过P点的圆C的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2df6b97f5eab4461e55a4ab9d04fdc87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33cc0f9aa168e43cc5759f017d69b498.png)
(1)求圆C的圆心坐标及半径;
(2)求过P点的圆C的切线方程.
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名校
解题方法
7 . 已知抛物线
上的三点
,B,C,直线AB,AC是圆
的两条切线,则直线BC的方程为____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ec68c680d1b8c8cfa98b48a27d2c46a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81550d38bd047ac4c6c0ffadc3712491.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/277e8382533e3ba18e213ea19ce6b9cb.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/30/96ae584d-41ad-4033-8665-1db4b86155fd.png?resizew=166)
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2024-01-30更新
|
301次组卷
|
2卷引用:江苏省镇江第一中学2022-2023学年高二上学期期末考试数学试题
8 . 已知圆O:
和圆C:
,圆心为点C,现给出如下结论,其中正确的个数是( )
①圆O与圆C有四条公切线
②过点C且在两坐标轴上截距相等的直线方程为
或![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
③过点C且与圆O相切的直线方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b10208f5af532e9b621cf113c688e14.png)
④P、Q分别为圆O和圆C上的动点,则
的最大值为
,最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51e5a3a88f7d166f2877a5bc22a6bca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de7acd2faeb5513785c3169d6b29dd1d.png)
①圆O与圆C有四条公切线
②过点C且在两坐标轴上截距相等的直线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00d816a6e4a5c6375309040fdda0038b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
③过点C且与圆O相切的直线方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6b10208f5af532e9b621cf113c688e14.png)
④P、Q分别为圆O和圆C上的动点,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6612d35ed52e5e28da9ee4cba4fd5b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d51e5a3a88f7d166f2877a5bc22a6bca.png)
A.0 | B.1 | C.2 | D.3 |
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解题方法
9 . 已知圆
,点
为直线
上一动点,过
点向圆
引两条切线
和
,其中
,
为切点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59f6ef25fb9949607b3e25fb1b8fa426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bf25e032b5599ac49383de06e776365.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf702adb116c1e46569eb7050d029f49.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.![]() ![]() |
B.![]() ![]() |
C.当![]() ![]() ![]() |
D.原点![]() ![]() |
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解题方法
10 . 已知圆
过点
,且圆心在直线
上,
(1)求圆
的方程:
(2)过
作圆
的切线,求切线方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf1179908fcf7cd469ec54cf40cf2ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad3a4d8eb0a4f3dd417124a19f60066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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