名校
1 . 已知圆
,直线l过点
.
(1)若直线l的斜率为
,求直线l被圆C所截得的弦长;
(2)若直线l与圆C相切,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca23a2a8cf7f1022133ee825c7e12ae8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2857f75cfb98c78e0d96dfd4d7d0240.png)
(1)若直线l的斜率为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/274a9dc37509f01c2606fb3086a46f4f.png)
(2)若直线l与圆C相切,求直线l的方程.
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2024-01-30更新
|
274次组卷
|
2卷引用:广东省广州市天河区2023-2024学年高二上学期期末数学试题
解题方法
2 . 已知圆C的圆心坐标为
,与直线
交于A,B两点,且
.
(1)求圆C的标准方程;
(2)求过点
的圆C的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80991c1f0c963104740e50cfff6f29a8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b979396a703fb14715ba39232f5786a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/529b4836786aca156de325464ea2ecd9.png)
(1)求圆C的标准方程;
(2)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b42d3a8480fb75c72594ea3ee9aa4970.png)
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2023高二上·全国·专题练习
3 . 已知圆M:
,点P是直线l:
上的一动点,过点P作圆M的切线PA、PB,切点为A、B.
(1)当切线PA的长度为
时,求点P的坐标;
(2)求线段AB长度的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4c2f9bc74275491cb5972fefdf4d98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3f52cb58b6bc5d71030463ba7e28134.png)
(1)当切线PA的长度为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
(2)求线段AB长度的最小值.
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解题方法
4 . 已知圆
过点
和
,且圆心
在直线
上.
(1)求圆
的标准方程;
(2)经过点
的直线
与圆
相切,求
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b5272ef0c7dc3d9574334fe68ecbaf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8fb59da24f78d282c87ed75d033dac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0985b973395bcd371cd1e26d3fcd1c36.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a9f1c6beba1c6584f0ffd6bfb812b15.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/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-26更新
|
323次组卷
|
5卷引用:河南省新乡市2023-2024学年高二上学期1月期末测试数学试题
名校
解题方法
5 . 已知圆C的方程为:
.
(1)若直线
与圆C相交于A、B两点,且
,求实数a的值;
(2)过点
作圆C的切线,求切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4561bfcd66d795bb656b2c190e44217.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4eaea2bcc76dbf8cb19729ae99a5683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/699fc9b7e879af4866aaa07848dfb423.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2595e01e8751886a27862cce04e2d1.png)
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解题方法
6 . 已知圆
.
(1)圆
与圆
交于
两点,求公共弦长
;
(2)直线
过点
且与圆
相切,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bce769d55393c86ae6c312de5158e4b3.png)
(1)圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e201e48c910c7364803cad8f42a19e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f9a3ea5e76e165faeabfdbc9717c287.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
7 . 已知圆
的半径为3,圆心
在直线
上,点
.
(1)若圆心
在
轴上,过点A作圆
的切线,求切线方程;
(2)若在圆
上存在点
,满足
(
为坐标原点),求圆心
的横坐标的取值范围.
![](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/026808536f6b6d265c778e23836fbf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a18a7caa080988802ba1145b4fe4203.png)
(1)若圆心
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若在圆
![](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/ed154dc722c0576255346d7f237969ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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解题方法
8 . 已知抛物线
:
(
)经过点
.
(1)求抛物线
的方程及其焦点坐标、准线方程;
(2)过抛物线
上一动点
作圆
:
的一条切线,切点为
,求切线长
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fc58c62444bf42a25289c45425a00f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5abd313d4e92a762fb7fb0c1cb65263d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d0924ff22fff9f5639feb0ceeece80d.png)
(1)求抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过抛物线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df0d79e42d86b0def4caa10dffa75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
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9 . 已知圆
.
(1)过点
作圆
的切线,求切线的斜率
(2)直线
与圆
交于
两点,
是
上的动点,求三角形
面积的最大值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c03843b03613ff8ab3267d2b7ad7f03.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a70feb95addc50c555e2eb6ad82521ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d5d58c8c55fc8dac4fcdf3221300316.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.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/7a855335176fc36a15017f50a8561348.png)
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解题方法
10 . 已知圆
经过点
和
,且圆心
在直线
上,
(1)求圆
的标准方程;
(2)过点
作圆
的切线
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ca979687ffb2214e747525635a6912c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5590337b3868db8523eeb7f448efcf05.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0947dc8f5ba116aaf3239d66adc7474.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f2583333c4b9aa85b4cdb64755f5179.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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