1 . 在平面直角坐标系
中,一条光线从点
时出,经直线
反射后,与圆
相切,写出一条反射后光线所在直线的方程______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4e9d81edef2b9140a79084e20b8ba0d.png)
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2 . 已知为抛物线
上一点,过
作圆
的两条切线,切点分别为
,
,则
的最小值为( )
A.![]() | B.![]() | C.![]() | D.![]() |
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2024·全国·模拟预测
3 . 对于任意的
,且
,均有定直线
与圆
相切,则直线
的方程为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22dd8b3dc4c609bab82d356a5cc2208d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c960b0019078a1e2723d623e83739fb9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4bd3516ad5b747980eb069c51b54e4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 古希腊著名数学家阿波罗尼斯发现了平面内到两个定点
的距离之比为定值
的点的轨迹是圆,此圆被称为“阿波罗尼斯圆”.在平面直角坐标系
中,已知
,点
满足
,设点
的轨迹为圆
,下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08f5d6f91366da27e9b96452bb04977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47be7ec43ae6cf4e4c25afa1a4fd1026.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/420d464c96149bd9cb5c7b1b3548133c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.圆![]() ![]() |
B.![]() ![]() |
C.过点A作直线![]() ![]() ![]() ![]() |
D.过点A向圆![]() ![]() |
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2024高三上·全国·专题练习
5 . (多选)在平面直角坐标系中,
,
,
,动点P满足
.则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8748dc55e2f45bc37fc4d84d7310f79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08ef03f452410ab19c6246567c427178.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc03af70a9f6f2509d2355cfadd0a968.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e06e23b4701e19c62dada4fa9566768.png)
A.点P的轨迹方程为![]() |
B.![]() |
C.过点C与点P的轨迹相切的直线只有1条 |
D.设![]() ![]() ![]() ![]() |
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2024·全国·模拟预测
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6 . 已知圆
关于直线
对称,过点
作圆
的两条切线,切点分别为
,
,则圆心
到直线
的距离为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1d42def67eb26b7cd0e057173242aee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdc523f751a40a21dece5645b15af9a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7d8cc13666ef5e288a3c98e2fc56aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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23-24高二上·江苏·单元测试
7 . 下列说法正确的是( )
A.直线![]() ![]() |
B.直线![]() ![]() ![]() |
C.若圆![]() ![]() ![]() ![]() ![]() |
D.若已知圆C:![]() ![]() ![]() |
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8 . 已知半径为
的圆
的圆心在
轴的正半轴上,且直线
与圆
相切.
(1)求圆
的标准方程;
(2)若
的坐标为
,过点
作圆
的两条切线,切点分别为
,求直线
的方程;
(3)过点
任作一条不与
轴垂直的直线与圆
相交于
两点,在
非正半轴上是否存在点
,使得
?若存在,求点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49e9d51742fcf0989adffaea9a17e73b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f96c46ef07e6012607a1a86d71554781.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a76df48990c036819c0cf7e57ef2aea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(3)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f911e0ed2429ab67c269cb0ff60ef218.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af99797a4b66560829f0eaf800627746.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6588aec7aa06aeae117c5c431c32054.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
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2024-01-08更新
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2卷引用:安徽省皖中名校联盟2024届高三上学期第五次联考数学试题
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9 . 已知圆
,点
在圆
上,过
可作
的两条切线,记切点分别为
,
,则下列结论正确的为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9edf67c2e68042e26faefd72455386c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48ac72a8d5a7c6e52dcab76cb9ea6074.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.若存在![]() ![]() ![]() ![]() |
D.若存在![]() ![]() ![]() ![]() ![]() |
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解题方法
10 . 已知圆心为C的圆经过点
和
,且圆心在直线
上,求:
(1)求圆心为C的圆的标准方程;
(2)若过点
作圆C的切线,求该切线方程;
(3)若圆C上恰有3个点到直线:
的距离为1,求实数m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21f20953302d861e6c698575bfbab1c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/292dd14f24b8392e499c328c1ca82f9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aefcbc03a5c916ebb20f891a0fe7e0d.png)
(1)求圆心为C的圆的标准方程;
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed18bd80c6c4142f68e89f4ad44570b5.png)
(3)若圆C上恰有3个点到直线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1970f9c78ed513e3710299ade4ac4bfe.png)
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2024-01-03更新
|
903次组卷
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3卷引用:山东省泰安市泰山外国语学校2024届高三上学期期末数学试题