名校
1 . 如图,在平面直角坐标系
中,点
,
,角
的顶点与坐标原点
重合,始边为
轴的非负半轴,终边与单位圆
交于点
,则阴影区域的面积的最大值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8950c7bc835103d52ceffab14b6b31a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3c3a0ff28cf69a2999d7af54d0792269.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/4/2/fcf79273-d183-44d9-9a97-720ec5bacbde.png?resizew=181)
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2 . 在平面直角坐标系中,定义
为点
到点
的“折线距离”.点O是坐标原点,点P在圆
上,点Q在直线
上.在这个定义下,给出下列结论:
①若点P的横坐标为
,则
; ②
的最大值是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
③
的最小值是2; ④
的最小值是![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
其中,所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/093c6d5bcaa69cea79b24688f5d1bd97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12a3efb79f35db8448f3391252ab7d4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8df332f01628130c084fd46aaca0a4b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8a39648cb8036d9773c2fcc145e6270.png)
①若点P的横坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94f8657de54481172ca9179c88c0c4c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ae1bf271f86fd36f7e07dfdc03a0f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3e32a237e5e2d4dc064d337ab21fef41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5120d563479e6e13dabfff4e09225d51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc9e3b3302ef30f5853224dc491ded16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
其中,所有正确结论的序号是
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3 . 设P,Q分别为直线
和圆
上的点,则
的最小值为__________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42498f6e0fc9a61c9857b70a87f02c5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afa2fc49351d3e40861e6425f726a796.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2023-12-11更新
|
308次组卷
|
6卷引用:北京市第一七一中学2023届高三上学期期中数学质量检测试题
名校
4 . 已知半径为
的圆
经过点
,则圆
上的点到直线
距离的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3654254401fc902c3cb4912969f21f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d984080283a1178e9a34b8911dc64a69.png)
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5 . 数学美的表现形式不同于自然美或艺术美那样直观,它蕴藏于特有的抽象概念,公式符号,推理论证,思维方法等之中,揭示了规律性,是一种科学的真实美.平面直角坐标系中,曲线
:
就是一条形状优美的曲线,对于此曲线,给出如下结论:
①曲线
关于坐标轴和直线
均对称;
②曲线
恰好经过4个整点(即横、纵坐标均为整数的点);
③曲线
围成的图形的面积是
;
④曲线
上的任意两点间的距离不超过4;
⑤若
是曲线
上任意一点,则
的最小值是2.
其中正确的结论序号是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f866a668cc68eac53dfa72454a6d4523.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d3051f43ac48c0a730a791b8a93ad37.png)
②曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
③曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55256c64b7c8f55539a3a3e4db488c54.png)
④曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
⑤若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82aaa597a5aa6176863eda3fdf83e181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38209addb9e6c73f9e82f9bd59bb3ca.png)
其中正确的结论序号是
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解题方法
6 . 法国数学家加斯帕•蒙日被称为“画法几何创始人”、“微分几何之父”.他发现与椭圆相切的两条互相垂直的切线的交点的轨迹是以该椭圆中心为圆心的圆,这个圆称为该椭圆的蒙日圆.若椭圆
的蒙日圆为
,过
上的动点
作
的两条切线,分别与
交于P,Q两点,直线
交
于A,B两点,则下列说法,正确的有______ .
①椭圆
的离心率为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
②
面积的最大值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b155facaed964aae6438f290a3cc0ed.png)
③
到
的左焦点的距离的最小值为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2eca4906dcaab3051394361d9552f1.png)
④若动点
在
上,将直线
,
的斜率分别记为
,
,则
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/163b5beef24f681605adecc6b0ba76e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c385c7c3482ce42ba4d5106bf865353e.png)
![](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/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
①椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
②
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b155facaed964aae6438f290a3cc0ed.png)
③
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b2eca4906dcaab3051394361d9552f1.png)
④若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67d822262ff00915910e5b87d81ad1ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d97dc3b752832906de41447bb58a341.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ddf41eff7a1310a7dcba4b236e0543ed.png)
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7 . 圆
上的点到直线
距离的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9df0d79e42d86b0def4caa10dffa75a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0947dc8f5ba116aaf3239d66adc7474.png)
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8 . 古希腊数学家阿波罗尼斯发现:平面内到两个定点A,B的距离之比为定
的点的轨迹是圆.人们将这个圆称为阿波罗尼斯圆,简称阿氏圆.已知
,
,动点M满足
,记动点M的轨迹为曲线W,给出下列四个结论:
①曲线W的方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f269f3d5e4148989d8897efa29cc60.png)
②曲线W上存在点D,使得D到点
距离为6;
③曲线W上存在点E,使得E到直线
的距离为
;
④曲线W上存在点F,使得F到点B与点
距离之和为8.
其中所有正确结论的序号是___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a08f5d6f91366da27e9b96452bb04977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae0d9116a9c839264169b933aac70d6e.png)
①曲线W的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7f269f3d5e4148989d8897efa29cc60.png)
②曲线W上存在点D,使得D到点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29343388ca8b33dc98325e65382b38a0.png)
③曲线W上存在点E,使得E到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5ab466aedd6e176088d8dee7bc3e3aaa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35361e76a7c85d1886728c8d0200b234.png)
④曲线W上存在点F,使得F到点B与点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd243fab0af865af67a2ab817e909cf5.png)
其中所有正确结论的序号是
您最近一年使用:0次
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9 . 若对于圆
上任意的点
,直线
上总存在不同两点
,
,使得
,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e50ce47d0602f3d0d5ec7803f76326ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a0521e43aed6757d73928ae82976461.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/210a836444e4d6e4e37a89e5f7a537eb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
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2022-11-07更新
|
1311次组卷
|
9卷引用:北京大兴精华学校2023届高三上学期12月月考数学试题
北京大兴精华学校2023届高三上学期12月月考数学试题福建省福州第三中学2023届高三上学期第三次质量检测数学试题(已下线)仿真演练综合能力测试(二)湖南省长沙市望城区第一中学2022-2023学年高二下学期期末模拟数学试题(已下线)模块三 专题9 直线与圆、圆与圆的位置关系 B能力卷(已下线)模块三 专题12 直线与圆、圆与圆的位置关系 B能力卷(已下线)高二上学期期中考试填空题压轴题50题专练-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)河南省周口市郸城县第一高级中学2023-2024学年高二上学期第一次月考数学试题四川省宜宾市第四中学校2023-2024学年高二上学期期末数学试题
名校
10 . 已知点
,
,动点
满足
,则点M到直线
的距离可以是___________ .(写出一个符合题意的整数值)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd99c5000629d7f49499d666e68f40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcf82d01c39fd2c96e1edba0ad37dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77bc22b148dd8c17a29b08c5ee7fe707.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026808536f6b6d265c778e23836fbf13.png)
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2022-06-02更新
|
1177次组卷
|
5卷引用:北京市第八十中学2022届高三下学期考前热身数学练习试题
北京市第八十中学2022届高三下学期考前热身数学练习试题直线与圆的方程中的高考新题型(已下线)专题36 直线与圆、圆与圆的位置关系-3(已下线)模块六 专题9 易错题目重组卷(安徽卷)广东省博罗县2023-2024学年高二上学期期中数学试题