23-24高二上·全国·课后作业
1 . 写出下列各圆的方程:
(1)圆心在原点的单位圆;
(2)圆心为
,半径是5;
(3)圆心为
,经过点
;
(4)圆心在x轴上,经过
与
两点.
(1)圆心在原点的单位圆;
(2)圆心为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
(3)圆心为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5265d99095b635f62c7915298ec0e963.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
(4)圆心在x轴上,经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/663d94efcc8a8a4b5a3563e94eb8fbb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e29d1b965ae2bc5329d02155bdc87cdb.png)
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2 . 在平面直角坐标系中点
,圆
的圆心在
轴正半轴上,半径为
,且直线
与圆
相切.
(1)求直线
的方程;
(2)求圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5ccf8d0d1510ea9021014e558fd5263.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(2)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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3 . 如图,已知点A、B的坐标分别是
,点C为线段AB上任一点,P、Q分别以AC和BC为直径的两圆
的外公切线的切点,求线段PQ的中点的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cc6456181b91be35ace52bca6b87a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c246e930a94d2cf023439b963242664.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/7/39d14ae4-9379-4992-a363-2edf7df525f7.png?resizew=248)
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解题方法
4 . 已知圆C经过(2,3)和(0,1)两点,再从条件①、条件②这两个条件中选择一个作为已知,解答以下问题
(1)求圆C的方程;
(2)过
的动直线
与圆C相交于
两点,当
时,求直线l的方程;条件①:圆心在x轴上方且与直线
相切;条件②:圆心C在直线
.
(1)求圆C的方程;
(2)过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/355c8e295cd0e7895a7bcabb31ebcf13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1576770308cd3a340859c462b557ed9.png)
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5 . (1)圆C:
与圆D:
的方程相减,得到直线方程:4x-10y+1=0,讨论该直线与已知两个圆的关系;
(2)将上述命题在曲线仍为圆的情况下加以推广,即要求得到一个更一般的命题,而已知命题应成为所推广命题的一个特例;
(3)椭圆方程
与曲线方程
相减,得到的方程是
,根据这个结果,你能得到什么结论?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e6ef45ac597bf0be21b270b202eab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f4d1302e7fbc2f2cb76b34b7d13b896.png)
(2)将上述命题在曲线仍为圆的情况下加以推广,即要求得到一个更一般的命题,而已知命题应成为所推广命题的一个特例;
(3)椭圆方程
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/676fa496027592e4a0972260e564ac60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b9f2de9e41b0a09d26bc0641feed1f80.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049e746876350620a694c8d399902523.png)
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6 . 如图,一艘海警船在O处发现了位于北偏东
,距离为6海里的海面上A处有两艘走私船,于是派遣巡逻艇追缉走私船,已知巡逻艇航速是走私船航速的2倍,且它们都是沿直线航行,但走私船可能向任意方向逃窜.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/23/64b37821-1fdd-4f6f-8f89-4f154e450397.png?resizew=159)
(1)求走私船所有可能被截获的点P在什么曲线上;
(2)开始追缉时发现两艘走私船向相反方向逃窜,速度为20海里/小时,其中一艘的航向为东偏南
,于是同时派遣了两艘巡逻艇分别追缉两艘走私船,两艘走私船被截获的地点分别为M,N,求M,N之间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be6a6301878fed2a01413020b27310a5.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/1/23/64b37821-1fdd-4f6f-8f89-4f154e450397.png?resizew=159)
(1)求走私船所有可能被截获的点P在什么曲线上;
(2)开始追缉时发现两艘走私船向相反方向逃窜,速度为20海里/小时,其中一艘的航向为东偏南
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
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2023-01-19更新
|
147次组卷
|
2卷引用:重庆市第十一中学校2022-2023学年高二上学期期中数学试题
名校
解题方法
7 . 在平面直角坐标系
中,点A,B的坐标分别为
.设曲线C上任意一点
满足
(
且
).
(1)求曲线C的方程,并指出此曲线的形状;
(2)对
的两个不同取值
,记对应的曲线为
.
(i)若曲线
关于某直线对称,求
的积;
(ii)若
,判断两曲线的位置关系,并说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f01b186ac8aa73e1a3609b40b6c3ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f47f265ff81a7a28ce17249647fc64f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3be362dec96173f246ff747264007817.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/472393b18c7880e73b40e31fbe2d951c.png)
(1)求曲线C的方程,并指出此曲线的形状;
(2)对
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d491ca1d69c14de489ec68aa280c97.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(i)若曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0d491ca1d69c14de489ec68aa280c97.png)
(ii)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56510aad1dc776f03ec75bca43954ef4.png)
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2022-12-16更新
|
170次组卷
|
2卷引用:浙江省杭州第四中学下沙校区2022-2023学年高二上学期期中数学试题
解题方法
8 . 已知直线l的倾斜角为
,且过点(3,3),直线l分别与x轴、y轴交于A,B两点,圆C是以AB为直径的圆.
(1)求圆C的标准方程;
(2)分别判断点M(6,4),点N(
1,1)与圆C的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd4c5016bd1fc6582078299b9cf8b392.png)
(1)求圆C的标准方程;
(2)分别判断点M(6,4),点N(
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bfc339cf6dd66599db64fa3fa44e608.png)
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名校
9 . 如图,已知点
是直线
上任意一点,点
是直线
上任意一点,连接
,在线段
上取点
使得
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/b55334fd-c7cb-42dc-b0c7-25fc3accba3b.png?resizew=217)
(1)求动点
的轨迹方程;
(2)已知点
,是否存在点
,使得
?若存在,求出点
的坐标;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9f0a54331c862854799cf40f2babe27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49696d0302f7c498b50cbbbae12e7db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92a3d0587624ba34116f436dde0265c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/14/b55334fd-c7cb-42dc-b0c7-25fc3accba3b.png?resizew=217)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4500d7d98cb3d03ff5651d0c412370e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d3306a9f91ee825bd2c4955ee800c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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名校
10 . 已知圆
经过坐标原点
,圆心为
;直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f96c39b2a6cbab5ae54da11210b6cf7.png)
(1)若
,记
为圆上的点到直线
的距离,求
的最大值;
(2)设直线
与圆
的相交弦为
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fa433c7f879181697b73c751605d394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f96c39b2a6cbab5ae54da11210b6cf7.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/500d68f2678989a5ce7431cfd51b019d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0276fc58eb6688d0c3711caeadd5b2bd.png)
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