名校
1 . 已知圆
及圆内一点
,P为圆M上的动点,以P为圆心,PA为半径的圆P.
(1)当
且P在第一象限时,求圆P的方程;
(2)若圆P与圆
恒有公共点,求r的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3eab13918e2a250c9a9eac092e6092.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f2b1f4120365cb6ee4925fe417563f9.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e13a63015fe678713b94f56d61f9addf.png)
(2)若圆P与圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aabf1608dd9ef8e8f00ffd2ebe4a82b.png)
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2 . 设点
为圆
上一点,已知点
,则下列结论正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b7f25834d8218c53cb975c2a2fe7442a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f011b653897003ff8c430af67c7c01f.png)
A.![]() ![]() |
B.![]() |
C.存在点![]() ![]() |
D.过A点作圆![]() ![]() |
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3 . 已知双曲线
(
,
),点
是
的右焦点,
的一条渐近线方程为
.
(1)求
的标准方程;
(2)过点
的直线与
的右支交于
两点,以
为直径的圆记为
,是否存在定圆与圆
内切?若存在,求出定圆的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67ca5fd57c2c2fcc3c7a574fdd1467d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a844e14cdc075e436a7ad919431b4c3.png)
![](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/45cc81cfaccc00aa4b7139de5a35a102.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ae1567d8f98fabc1a3948f8602cc5e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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2024高二上·全国·专题练习
4 . 已知圆
,
,动圆
与
,
都相切,则动圆C的圆心轨迹E的方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1daeb4296576f4728bf387dbfa726874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd7feb61317950d7b6abc1464f309361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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5 . 已知圆
,圆
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70feca8eac775ebee7b6d9760e2be6f6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cddb2b6c3d263c66cc83804ed6b4bac9.png)
A.若圆![]() ![]() ![]() |
B.当![]() ![]() ![]() |
C.当![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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6 . 已知圆
,圆
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/021b808a21cb6be07be8b83777eabba9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d645681e7f93173c815b1cfabdf883c.png)
A.若点![]() ![]() ![]() |
B.若圆![]() ![]() ![]() |
C.圆![]() ![]() |
D.过点![]() ![]() ![]() ![]() ![]() ![]() |
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名校
7 . 已知圆
,则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb6e9693f41a982230a768aab99df9e.png)
A.圆![]() ![]() |
B.圆![]() ![]() ![]() ![]() |
C.圆![]() ![]() ![]() |
D.动点![]() ![]() ![]() |
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8 . 已知圆
:
与圆
:
相交于A,B两点,则下列判断正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1376bc360486059a9674a964d031e9ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28da6766230aeb546a2588daf93958ff.png)
A.两圆的相交弦所在直线方程为![]() |
B.两圆的公共弦长为![]() |
C.经过A,B两点,且过原点的圆的方程为![]() |
D.P为![]() ![]() ![]() |
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9 . 已知点
为坐标原点,
的直径为2,点
,点
是
:
上的动点,记线段
的中点
的轨迹为Γ.
(1)求Γ的方程;
(2)判断Γ与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fef27cb7cb1b666c1734c65a7aa9aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1d00483a05dd88fbd59cd2c95dbaf68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求Γ的方程;
(2)判断Γ与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
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10 . 圆
与圆
的公共弦长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19da0e222aa85416535ece3ca66911b9.png)
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