解题方法
1 . “曼哈顿距离”是人脸识别中的一种重要测距方式,其定义如下:设
,
,则
,
两点间的曼哈顿距离
已知
,点
在圆
上运动,若点
满足
,则
的最大值为_________ .
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c04bbc507d8f917da5253fca7f2c9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a5862f87bdbd8d6c653905cddb9900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f6ae1c2a81078eac5ed2f4f823b671.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b83e2fc66e8ab0e6f60a1790cea6c1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de86d9c0675d246a280f6b71a68aaf9d.png)
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2 . 已知点
,
,点
在直线
上,则
的最小值为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ee9c730266ecf448c14608e24d37b986.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08e8486793a64665b63323e33f3b8386.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c960fc862fd36db83082f5c50cd604b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a13ec9a812274ad0839f20ba17348687.png)
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3 . “曼哈顿距离”是十九世纪的赫尔曼·闵可夫斯基所创,定义如下:在直角坐标平面上任意两点
,
的“曼哈顿距离”为
,已知动点N在圆
上,定点
,则M,N两点的“曼哈顿距离”的最大值为______ .
![](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/42854888631f64eeeb221f9a327e5b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/651ca79886cf911c55c48cba2a6a2acd.png)
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4 . 若实数
满足
,则
的最大值是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2d538c852950edc0d843094effa89b1.png)
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解题方法
5 . 已知椭圆
的右焦点为
是
的中点,若椭圆
上到点
的距离最小的点有且仅有一个,则椭圆
的离心率的取值范围为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a56afb8c84a2105d525b84b6862a5426.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cad4595d5352b2884568a59d8d766a4.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/c5db41a1f31d6baee7c69990811edb9f.png)
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6 . 在直线
上求一点,使它到原点的距离和到直线
的距离相等,则此点的坐标是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/710c58628d4a3990ac8347dfa2d2ca7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5ed34fb976d59e36f5ae68ba97f5ff2.png)
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2023-12-09更新
|
173次组卷
|
3卷引用:江苏省南京市励志高级中学2023-2024学年高二上学期期末复习数学试题
解题方法
7 . 费马原理是几何光学中的重要原理,可以推导出圆锥曲线的一些光学性质.点P为椭圆(
,
为焦点)上一点,点P处的切线平分
外角.已知椭圆
,O为坐标原点,l是点
处的切线,过左焦点
作l的垂线,垂足为M,则线段
的长为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a818c7b7f571f7173feb9b73424d5ffe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a1eb15d354e4ef64e6f4297edc8acd5.png)
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8 . 设
,过定点
的动直线
和过定点
的动直线
交于点
,则
的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e72f6b2ef3329828cb8fc873eeba7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/781667893437245d21db9a2e66f3539e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/757f055a6bb9317021f66beb82ecfcd5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf2d50a03130b0d6036f8354b81b7243.png)
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2023-11-17更新
|
533次组卷
|
4卷引用:江苏省常熟市2023-2024学年高二上学期期中数学试题
江苏省常熟市2023-2024学年高二上学期期中数学试题江苏省苏州市常熟省中2023-2024学年高二上学期期中数学试题(已下线)2.3.1 两条直线的交点坐标、两点间的距离公式【第三课】四川省眉山市彭山区第一中学2023-2024学年高二上学期12月月考数学试题
解题方法
9 . 已知O为坐标原点,
,Q为抛物线
上任意一点,且
恒成立,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54259096ec6358dd555baf9510d43971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e8953ded144195804384dcb494d5e2a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5785a7a692b9f340706da1aa1adea245.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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10 . 已知圆
:
和点
,若圆
上存在两点
,
使得
,则实数
的取值范围是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3c6a0d4ef4cc7fea93adc9d5639ab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/480d82e30ad56a7eaa67de5ddf627695.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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