1 . 阿波罗尼斯与阿基米德、欧几里得被称为亚历山大时期数学三巨匠.“阿波罗尼斯圆”是他的代表成果之一:平面上一点
到两定点
的距离之满足
为常数,则
点的轨迹为圆.已知圆
:
和
,若定点
(
)和常数
满足:对圆
上任意一点
,都有
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b981a38ddc94e2806871d7e8a17290d.png)
_________ , ![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d747dfb35d6eef859a1a325bcb06f5.png)
___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4f743963fe375a858182cb35ba7fb9f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b9ac996c3ee6b505a1061ad13a96177.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389e9f5b9760aeb8ba7c459db61f1d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8f4c59dad97e66c4e918cb88c910da0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b981a38ddc94e2806871d7e8a17290d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7d747dfb35d6eef859a1a325bcb06f5.png)
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2020·浙江·三模
2 . 大约在2000多年前,由我国的墨子给出圆的概念:“一中同长也”意思是说,圆有一个圆心,圆心到圆周的长都相等,这个定义比希腊数学家欧几里得给圆下定义要早100年,已知
为原点,
,若
,则线段
长的最小值为_____________
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7fb72e05dfe865a94667b0255cfb9ed1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea6fd3914d9da656c8d0225a084eef5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
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3 . 若平面内动点
到两定点
的距离之比
(其中
为常数,
),则动点
的轨迹为圆,这个轨迹最先由古希腊数学家阿波罗尼斯发现的,故称作阿波罗尼斯圆.若已知
,则此阿波罗尼斯圆的方程为_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f8b7a5b9d5eacb31cd778fe8c61ebf9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1758ec2d7ee9c5a240900e00b3472ca9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8b0181b978b67c7a12ef22ae91ce189.png)
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