名校
解题方法
1 . 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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2 . 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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名校
解题方法
3 . 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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名校
解题方法
4 . 已知圆心C在直线
上,圆C过点
,
.
(1)求圆C的标准方程;
(2)已知点
,求过点M的圆C的切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e894db81047f81df006964a290c039cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4193c0af60bce74c8f575dc8dc3ea0a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80a0066672fdf6e591b842847e5a6c7c.png)
(1)求圆C的标准方程;
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25ce60648ea5042ab5eb5702efe651a.png)
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名校
5 . 在平面直角坐标系
中,圆
的半径为
,其圆心在射线
上,且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e058ef2a64b0d5a5a5ce4c6c8a028aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求圆
的标准方程;
(2)若直线
过点
, 且与圆
相切,求直线
的方程;
(3)自点
发出的光线
射到
轴上,被
轴反射,其反射光线所在的直线与圆
相切,求光线
所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cfb764b285362ee742b6dc613a1460a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e058ef2a64b0d5a5a5ce4c6c8a028aed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c90282d4a37c9a20620d4bbb0c263cae.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e9b5e076078240e0c5ad9763a9824d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(3)自点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c058a8ba318315dde9c5a0392944b4b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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名校
解题方法
6 . 已知圆C:
.
(1)求过点
且与圆C相切的直线方程;
(2)求圆心在直线
上,并且经过圆C与圆Q:
的交点的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85300de5f398c86e24b52e0a2298f6a9.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c36d02c9e0fecab6c546da6473d32912.png)
(2)求圆心在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0f7fbfa2214ca72495a993b2fed8b61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/331a133d2fff3d6e402f25143167fba9.png)
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2024-02-03更新
|
84次组卷
|
2卷引用:云南省玉溪第一中学2023-2024学年高二上学期期中考试数学试卷
2023高二上·全国·专题练习
7 . 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
8 . 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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名校
解题方法
9 . 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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2023高二上·全国·专题练习
解题方法
10 . 已知圆
.
(1)若不过原点的直线
与圆
相切,且在
轴,
轴上的截距相等,求直线
的方程;
(2)从圆
外一点
向圆引一条切线,切点为
为坐标原点,且有
,求点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f97d9a51394b190f99b75bd277178ffc.png)
(1)若不过原点的直线
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)从圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da8255e035cfd3c2e84f10b236b6fd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e0cac807d10c3dc2f00f29d1687f7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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