解题方法
1 . 在平面直角坐标系
中,已知直线
:
与圆
:
交于
两点,则
的最大值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da08d6d27b6cf7ee1a9f49737bbb70de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a324c816e299f545ba3f31d37544d07d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a704469569b68ee11ab166dba3f686f0.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2 . 已知
,若平面内满足到直线
的距离为1的点
有且只有3个,则实数![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e18fd813ef878b9d7292620c757f43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/692265c4b64c721bd3e567b8af832b7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6c57bbef89a37f1a3808c0ceeac0c22.png)
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2024-04-17更新
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6卷引用:江苏省苏锡常镇四市2024届高三下学期教学情况调研考试数学试题
3 . 已知点
在圆
上,点
,
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d2025bac7b08ec9f206cfce02bdd7ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/243e699ef05dc31d5f577bef2a22801e.png)
A.存在点![]() ![]() | B.![]() |
C.存在点![]() ![]() | D.![]() |
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4 . 已知定圆
,点A是圆M所在平面内一定点,点P是圆M上的动点,若线段
的中垂线交直线
于点Q,则点Q的轨迹可能为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0d815b1dd40ac542b3a9d10584da5d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
A.椭圆 | B.双曲线 | C.抛物线 | D.圆 |
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3卷引用:江苏省四校联合2024届高三新题型适应性考试数学试题
解题方法
5 . 已知圆
经过
中的三点,且半径最大.
(1)求圆
的方程;
(2)过点
的直线与圆
交于
两点(
在
轴上方),在
轴上是否存在定点
,使得
轴平分
?若存在,请求出点
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b66ec9bf41dcc5784431ed5630f5261.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea5b6926cdb99eb58070b8720718f71a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5e8e435259ab192d798bb8bf7774cdf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
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6 . 已知线段AB的端点B的坐标是
,端点A的运动轨迹是曲线C,线段AB的中点M的轨迹方程是
.
(1)求曲线C的方程;
(2)已知斜率为k的直线l与曲线C相交于两点E,F(异于原点O),直线OE,OF的斜率分别为
,且
,
①证明:直线l过定点P,并求出点P的坐标;
②若
,D为垂足,证明:存在定点Q,使得
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d02dba7080b2d1e0d7a4a16a48a0d47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5d1ac5adb13362206cfc2f2fb624d30.png)
(1)求曲线C的方程;
(2)已知斜率为k的直线l与曲线C相交于两点E,F(异于原点O),直线OE,OF的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73849df3a825a25491e0e18f846d9904.png)
①证明:直线l过定点P,并求出点P的坐标;
②若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8aed88ad640f3d76735f1e5dbc04b23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4110cc2b5dc3aabd585a8e9a81855a12.png)
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7 . 在平面直角坐标系
中,已知圆C的圆心在
上,且圆C与x轴相切,直线
,
.
(1)若直线
与圆C相切,求a的值;
(2)若直线
与圆C相交于A,B两点,将圆C分成的两段弧的弧长之比为
,且
,求圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bfea30b3df4214f447aaeacbf558aa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80b138b5a47d97be0b954020002d9033.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/30dd809d2f4f4f2287043eac970bf526.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fc5881f1ce9b4172ca346032d0fd1e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c48119b3932497634478f656c752ec4.png)
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|
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2卷引用:江苏省南京市2023-2024学年高二上学期期中调研测试数学试题
解题方法
8 . 长方体
中,
,
,上底面
的中心为
,当点
在线段
上从
移动到
时,点
在平面
上的射影
的轨迹长度为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3da8c338342e38c9aa3f274c053fd5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4957406b21df59fdf7fa184752287b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1b90bf8b51db7a4ff6e0678bd3d1ea0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d609847e2ff3d64e5a514582c3ead0e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20ecac2dad4cffdd971fd23deacff3fc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12fe32dfbd66709875c5b9f79c9496da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34be4e71cabf458f17a6cd7f24bc70af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
A.![]() | B.![]() | C.![]() | D. ![]() |
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9 . 直线
与曲线
恰有两个交点,则实数m的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12f9bd7fdb0c44b5e2e1d5a59dd6f7dd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/75db6f4115857bc0041da949ba5f95a9.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2卷引用:江苏省无锡市江阴市某校2023-2024学年高二上学期10月学情调研数学试题
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10 . 若点
在圆
外,则实数
的取值范围为________ ;
分别在直线
与直线
上,且
.当圆
的半径为3时,已知点
,则
的最小值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4cd84a4d9bb73ab5cb402cbc721bf5b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5b1b15a4605fce993cb13aefbf40360.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b7f07637cafd4bdb7bc0eaa5b1eeaca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73aa23d5bae655a13ecad8f97505dbe7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8966c9cc4fa4ff537a546bcd0b055554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb5133b81d5ba51a3cd1e0f6882f5523.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c581bdb94840715012544d1b18dc18fb.png)
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