对于半径为
的
及一个正方形给出如下定义:若
上存在到此正方形四条边距离都相等的点,则称
是该正方形的“等距圆”。如图1,在平面直角坐标系
中,正方形
的顶点
的坐标为(2,4),顶点
、
在
轴上,且点
在点
的左侧.
(1)当
时,已知两点
,
,则可以成为正方形
的“等距圆”的圆心的是________;
(2)如图2,在正方形
所在平面直角坐标系
中,正方形
的顶点
的坐标为(6,2),顶点
,
在
轴上,且点
在点
的上方.若
同时为上述两个正方形的“等距圆”,且
与
所在直线相切,求圆心
的坐标;
(3)在(2)的条件下,将正方形
绕着点
旋转一周,在旋转的过程中,线段
上没有一个点能成为它的“等距圆”的圆心,写出
的取值范围.(不必说明理由)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59052cd76ae33d80ad2400bee7a9cb63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13f923d1246ba30971102a8c7523c939.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2956db0b41ca80c40681e32bceeb86ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
(2)如图2,在正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/611f100dcfa7803db6eb233e2e7f2dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d1d9218917d85a1dc19e60f076b8bfa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(3)在(2)的条件下,将正方形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b39addc1173a458af87ed5c5e3f06466.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/2/87c1381f-9be2-4161-b69d-22fb1c64cc7f.png?resizew=334)
更新时间:2020-08-07 17:42:41
|
相似题推荐
解答题-问答题
|
较难
(0.4)
解题方法
【推荐1】已知抛物线
,抛物线上的点
到焦点的距离为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/2fd3f6eb-cb53-4ddb-a4b6-788d53688697.png?resizew=175)
(1)求抛物线的方程和
的值;
(2)如图,
是抛物线上的一点,过
作圆
的两条切线交
轴于
,
两点,若
的面积为
,求点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8516f71467b419293fa27df70bdaed74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b5ab73897d6a3fb4d500d3e55944742.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/3/2fd3f6eb-cb53-4ddb-a4b6-788d53688697.png?resizew=175)
(1)求抛物线的方程和
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)如图,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eefebc1e98817bfe7e835da7a1a0d6c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/c41663d9e5e18891475aeaa98794f33d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6e196d3c447cb1007ae8d0adcefb46a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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【推荐2】如图,经过原点O的直线与圆
相交于A,B两点,过点
且与
垂直的直线与圆M的另一个交点为D.
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/639e314a-8eb4-436b-a4a0-9bce7f52422c.png?resizew=171)
(1)当点B坐标为
时,求直线
的方程;
(2)记点A关于x轴对称点为F(异于点A,B),求证:直线
恒过x轴上一定点,并求出该定点坐标;
(3)求四边形
的面积S的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e56c7e28200ecc48ddc4951fbd22caa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cce0e2c31b225af20c18fbd3d116ee09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b79dd200766db27fb90d6bd1992cf658.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/29/639e314a-8eb4-436b-a4a0-9bce7f52422c.png?resizew=171)
(1)当点B坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6919218ef8f87540bd91c8b0ba02e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1ffb98f1e3c1317c0db403d3af04bdc.png)
(2)记点A关于x轴对称点为F(异于点A,B),求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c4eccda4edcee29a5f15609e85106df.png)
(3)求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cb3f9a5da641be35117fd35ba07a6aa.png)
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解答题-问答题
|
较难
(0.4)
名校
【推荐1】已知点
,
,动点
满足
,记M的轨迹为曲线C.
(1)求曲线C的方程;
(2)过坐标原点O的直线l交C于P、Q两点,点P在第一象限,
轴,垂足为H.连结QH并延长交C于点R.
(i)设O到直线QH的距离为d.求d的取值范围;
(ii)求
面积的最大值及此时直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/993769b494e12c21dff0ee7c53a4a49f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96e30645f36e8628b9e25d53598d5174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef90f9574be26362fec2c2720f1be5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad9fdf8b318ddf822775a61ff26eb8a3.png)
(1)求曲线C的方程;
(2)过坐标原点O的直线l交C于P、Q两点,点P在第一象限,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59fbd9b5e5d8be69373850d7faebdaf1.png)
(i)设O到直线QH的距离为d.求d的取值范围;
(ii)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
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解答题-问答题
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(0.4)
名校
【推荐2】已知线段AB的端点B的坐标是(4,2),端点A在圆C:(x+2)2+y2=16上运动.
(1)求线段AB的中点的轨迹方程H.
(2)判断(1)中轨迹H与圆C的位置关系.
(3)过点P(3,2)作两条相互垂直的直线MN,EF,分别交(1)中轨迹H于M,N和E,F,求四边形MNFE面积的最大值
(1)求线段AB的中点的轨迹方程H.
(2)判断(1)中轨迹H与圆C的位置关系.
(3)过点P(3,2)作两条相互垂直的直线MN,EF,分别交(1)中轨迹H于M,N和E,F,求四边形MNFE面积的最大值
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解答题-问答题
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(0.4)
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【推荐3】为解决城市的拥堵问题,某城市准备对现有的一条穿城公路MON进行分流,已知穿城公路MON自西向东到达城市中心点O后转向东北方向(即
).现准备修建一条城市高架道路L,L在MO上设一出入口A,在ON上设一出入口B.假设高架道路L在AB部分为直线段,且要求市中心O与AB的距离为10km.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/e6485ac8-6fc3-4af9-a307-ecf8f6b59d3f.png?resizew=250)
(1)求两站点A,B之间距离的最小值;
(2)公路MO段上距离市中心O30km处有一古建筑群C,为保护古建筑群,设立一个以C为圆心,5km为半径的圆形保护区.则如何在古建筑群C和市中心O之间设计出入口A,才能使高架道路L及其延伸段不经过保护区(不包括临界状态)?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ce9433909d7423bcb7a2a8dbc410790.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/21/e6485ac8-6fc3-4af9-a307-ecf8f6b59d3f.png?resizew=250)
(1)求两站点A,B之间距离的最小值;
(2)公路MO段上距离市中心O30km处有一古建筑群C,为保护古建筑群,设立一个以C为圆心,5km为半径的圆形保护区.则如何在古建筑群C和市中心O之间设计出入口A,才能使高架道路L及其延伸段不经过保护区(不包括临界状态)?
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