1 . 已知点
是直线
上一动点,
与
是圆C:
的两条切线,M、N为切点,则四边形
的最小面积为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44ee82573986d4fa6a7ee1b5f397edae.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/650353eda77d014bb42d185bd967e549.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd8b64ef4c3a8c2382adb986d302c74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3029ea5516e56e8d20594c71929624f.png)
A.4 | B.![]() | C.2 | D.1 |
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解题方法
2 . 已知圆
的方程是
,
(1)若点
为圆
上一点,过点M作圆
的切线,求该切线方程.
(2)若点
为圆
外一点,过点M作圆
的两条切线,切点分别为A、B,
①求直线AB的方程.
②若
为直线
上的一个动点,试讨论直线AB是否恒过定点,若是,求出定点坐标;若不是,请说明理由
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
①求直线AB的方程.
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3511cdc6a9b56bc1d9415d3d94ef0f67.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f049d6f117b0ab3459ae444350dd66be.png)
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解题方法
3 . 在平面直角坐标系中,O为坐标原点,
(
),圆M:
.
(1)若
,过点A作圆M的切线,求此切线的方程;
(2)若在圆M上存在唯一一点P,使
,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c704999a090103f18c8e1b46ededca35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df0d79e42d86b0def4caa10dffa75a.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2a51944c720568f35d443589dfc1aa.png)
(2)若在圆M上存在唯一一点P,使
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/297af2859ce6975fe9cbff4158300d2d.png)
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4 . 在平面上,动点
与两定点
满足
(
且
),则
的轨迹是个圆,这个圆称作为阿波罗尼斯圆.已知动点
与两定点
满足
,记
的轨迹为圆
.则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00e5b80107ef1ece0ad477a7f2703d59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/51a8eb194c397afdb40737d432f87266.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a06966dee4fbf74f02543337fd04efcc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64929a846d98c92dc5a51e4927b0f99a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.圆![]() ![]() |
B.过点![]() ![]() ![]() |
C.过点![]() ![]() ![]() |
D.直线![]() ![]() ![]() ![]() ![]() |
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解题方法
5 . 已知圆
,动直线
过点
,下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/521d2cbdff8483ebba708857163ef1d9.png)
A.当![]() ![]() ![]() ![]() |
B.点![]() ![]() |
C.点![]() ![]() |
D.若点![]() ![]() ![]() ![]() ![]() ![]() |
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2024-02-12更新
|
94次组卷
|
2卷引用:内蒙古赤峰市松山区赤峰学院附属中学2023-2024学年高二上学期1月期末数学试题
6 . 已知圆
的圆心为
,过直线
上一点
作圆的切线,且切线段长的最小值为2.
(1)求圆
的标准方程;
(2)若圆
与圆
:
相交于
,
两点,求两圆公共弦
的长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d4cb0990b93c9900bab2784bef4b10f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(1)求圆
![](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/39e210795a966bd5dc1293479ab1988b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2824f7742d8b19c71173704addc50e08.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2024-02-12更新
|
111次组卷
|
2卷引用:河南省郑州市2023-2024学年高二上学期1月期末考试数学试题
7 . 已知圆
和圆
是圆
上一点,
是圆
上一点,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f96a501c261f723d67d4df10d82602.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b5429142c872401dff899623ae4904a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
A.圆![]() ![]() |
B.两圆的公共弦所在的直线方程为![]() |
C.![]() |
D.若![]() ![]() ![]() ![]() |
您最近一年使用:0次
2024-02-12更新
|
133次组卷
|
2卷引用:陕西省西安市莲湖区2023-2024学年高二上学期期末质量监测数学试题
8 . 已知圆
和圆外一点
,过点
作圆
的切线
,其中
是切点,则下列结论错误的是( ).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e3d143aea2ded268f1c6ea6b0dd0e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5de78b493bc2cc9696c584325c22ee7.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/790ef3382b1c731f2885eecfd92c2a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
A.![]() | B.![]() |
C.四边形![]() | D.点![]() ![]() |
您最近一年使用:0次
9 . 自圆
外一点
引该圆的一条切线,切线长等于点
到原点
的长,则点
的轨迹方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/626dd1e38f856778c2d3a987561b5d5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.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/dad2a36927223bd70f426ba06aea4b45.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 过点
作圆O:
的两条切线,则两条切线夹角的正弦值为______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f13bf66fc845b115de4ec45b4be0e23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
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