1 . 已知过点
的直线
与圆
交于
两点,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ae6b62c3779911fbc432a37781dba00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb278a8366633d8e8b8f5dab1fa1c08c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 一条直线经过点
,被圆
截得的弦长等于8,这条直线的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75bb708d1450f9222c3a3a6d7682e06c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a143573e9fe53e6a861154bf5b4c27c3.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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解题方法
3 . 已知圆
经过点
和
,且圆心
在直线
上.
(1)求圆
的方程;
(2)过点
的直线
与圆
相交于
,
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/e0c21dde2ad1e31c337bfb78c810ccb5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49cba284d675a3028d7a8d54f1f8ae70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e8a3365e99f926b1dafa901ab232152.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c2f21b1baf0624482fd41d7ba390341.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a14a85d5d71e238da9f4e499faec0f30.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 已知圆O:
,点M是圆O上任意一点,M在x轴上的射影为N,点P满足
,记点P的轨迹为E.
(1)求曲线E的方程;
(2)已知
,过F的直线m与曲线E交于A,B两点,过F且与m垂直的直线n与圆O交于C,D两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21d7d2366815548f1b5340e01c8311b1.png)
(1)求曲线E的方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532fb9d8a0715b513e9e3f144ea264e9.png)
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5 . 已知
是圆
上两个不同动点,直线
恒过定点
,若以
为直径的圆过点
,则
最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5aa69fd8445d01c98634c2e885b47d5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc12c55f2676aeb4f696f4a84e4d65b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fd316149b93724cda0cdc32e4bb3bd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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6 . 已知抛物线
的焦点为
,点
是抛物线
上一点,圆
与线段
相交于点
,且被直线
截得的弦长为
,若
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc025d879239f23396905b6b903ed703.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8049a6c0dce17ad81f6da99bff71cc5c.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/907d5147cea4c9ce855074864fe54506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3bf1c935b01eed783fe5e24fceff383.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a94367c41f40b35088f9ab3b84f3a37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e273ea2c1a107e9d9086eb417b20a6aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff24d4627c643c5aeee873c6e1e626aa.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7 . 已知直线
:
和圆
:
交于A,B两点,则弦AB所对的圆心角的余弦值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd38ef176b1bc2c4dbac8c4d98e8ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c82a1fed135888e1c072bc5078fc8a5.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
8 . 若双曲线
的一条渐近线被圆
所截得的弦长为
,则双曲线
的离心率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a2cfa22139b3e9c9a73500e1ba19f52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b90a620d8be40786ed98e78c1a81f48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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9 . “康威圆定理”是英国数学家约翰·威廉引以为豪的研究成果之一,定理的内容如下:如图,
的三条边长分别为
,
,
.延长线段
至点
,使得
,延长线段
至点
,使得
,以此类推得到点
,
,
,
,那么这六个点共圆,这个圆称为康威圆.已知
,
,
,则由
生成的康威圆的半径为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef5fcdbfc6293db5e91e6f1bcb46e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fefc41ca7ac455b9212f03322474591.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1c3fa6a68a9ffe7568996974b592f7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9abaeba15f3abdd877bc701af52c5cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee4c6c5446384bcc1306c342334c317f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18b3edb5d3ae89120085259d53265ab7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c01fdc7bc471af0b264a04aef0823e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43a71fc9c0068109dad1382354570665.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22a688b51f4862f610d3064199aeb336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23725094c363fd158166a8698971694c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1659bc969a9689f94a1d5a567fb29394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/10/78cdf7d8-a1fb-4a13-82e7-f171a0df28d4.png?resizew=175)
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10 . 已知
,
是圆O:
上两点,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d06402d2fc77d355868a917ea9863899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b4d40228d6e3f0d1a130f02044f3443.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
A.若![]() ![]() |
B.若点O到直线AB的距离为![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
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