1 . 在平面直角坐标系
内,O为坐标原点,对于任意两点
,定义它们之间的“曼哈顿距离”为
,以对于平面上任意一点P,若
,则动点P的轨迹长度为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56998322ea32b68685df4fef7b46912e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ed144a854178707c98cc51cdfaae852.png)
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2024-02-23更新
|
191次组卷
|
2卷引用:安徽省合肥市第九中学2023-2024学年高二上学期第二次单元检测数学试题
2 . “曼哈顿距离”是十九世纪的赫尔曼•闵可夫斯基所创词汇,定义如下:在直角坐标平面上任意两点
的曼哈顿距离为:
.已知点
在圆
上,点
在直线
上,则
的最小值为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e3a1467ecf286e3cadaf5aa006606f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c913b3abbf53d81fcf25bf83d4ae3756.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97adee14e22d459caa19a445ba41c165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57d7224242ab75080dfb394a39ebf7f8.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2023-12-03更新
|
1472次组卷
|
6卷引用:安徽省阜阳市第三中学2023-2024学年高二上学期二调考试(12月)数学试题
安徽省阜阳市第三中学2023-2024学年高二上学期二调考试(12月)数学试题(已下线)河南省信阳市信阳高级中学2023-2024学年高二上学期1月测试数学试题新疆生产建设兵团第三师图木舒克市第一中学2023-2024学年高二下学期数学开学考试数学试卷河北省部分学校2024届高三上学期摸底考试数学试题(已下线)压轴题三角函数新定义题(九省联考第19题模式)讲(已下线)(新高考新结构)2024年高考数学模拟卷(三)
3 . 在平面直角坐标系中,设点
,定义
,其中
为坐标原点.对于下列结论:
(1)符合
的点
的轨迹围成的图形的面积为
;
(2)设点
是直线:
上任意一点,则
;
(3)设点
是直线:
上任意一点,则“使得
最小的点
有无数个”的充要条件是“
”;
(4)设点
是椭圆
上任意一点,则
.
其中正确的结论序号为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e06125c200fde1bdbb2de12bab766548.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)符合
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27444dc732416f275764006abc9813a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4f337751613ef04450c28639a7d6d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f9093ebc69cdc03d8cca77a78ae561b.png)
(3)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cab240529c124eaabb995eda8db81e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cef44b80079073591bdea561208b2d61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2015d9a88fb4d8f0520790693abc9649.png)
(4)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b23a257b491367ffa232afbb7d10415.png)
其中正确的结论序号为( )
A.(1)、(2)、(3) | B.(1)、(3)、(4) |
C.(2)、(3)、(4) | D.(1)、(2)、(4) |
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4 . 定义点
、
之间的“直角距离”为
,若点
到点
的“直角距离”等于
,其中
、
满足
,
,则所有满足条件的点
的轨迹的长度之和为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a1b0a3ba474ddfd3175c983fa04d945.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2f109ad046f362d8686c7ef9810c568.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1282cc43ebf4b459832fec04d805989.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.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/be48cd4158fb76190935ab143de02ba3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2c06bfd29a2dd227412dbc9af54815.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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