解题方法
1 . 已知
为坐标原点,过点
的直线
与抛物线C:
交于
两点.
(1)证明:
;
(2)若
与坐标轴不平行,且
关于
轴的对称点为
,圆
:
,证明:直线
恒与圆
相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b072ff6d1b83232bebd7d4709ffba4ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/894c9c9109361963cf5196f89c1f2d18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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3卷引用:安徽省六安市叶集皖西当代中学2023-2024学年高二下学期3月月考数学试题
名校
2 . 已知圆
,直线
.
(1)求证:对
,直线
与圆
总有两个不同的交点;
(2)直线
与圆
交于
两点,当弦长AB最短时,求直线AB方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c406915922045153a67d269f41ac4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3445947fa34dd409a1354786e6c4a579.png)
(1)求证:对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/01c74a907dda6bb7d9d56d009d9df253.png)
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3卷引用:安徽省六安市第一中学2021-2022学年高二下学期开学考试数学试题
解题方法
3 . 已知圆C经过两点
,且圆心C在直线
上,直线l的方程为
.
(1)求圆C的方程;
(2)证明:直线l与圆C一定相交;
(3)求直线l被圆C截得的弦长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/743a22685aad638418aa50bbab5a00a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e35701dd16dbf6ec916064880b8b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/135727cec1ebb852664fd582a600babe.png)
(1)求圆C的方程;
(2)证明:直线l与圆C一定相交;
(3)求直线l被圆C截得的弦长的取值范围.
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2卷引用:安徽省六安市皖西中学2020-2021学年高二上学期期中文科数学试题
名校
4 . 已知圆
经过两点
,且圆心在直线
上,直线
的方程为
.
(1)求圆
的方程;
(2)证明:直线
与圆
恒相交;
(3)求直线
被圆
截得的弦长的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8c695f4ad0e78d81283475276cafd6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12e35701dd16dbf6ec916064880b8b52.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff2ffc762aa0e32a641a4e15d732dc75.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(3)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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