名校
1 . 已知圆C过点
,且与圆
外切于点
,
是x轴上的一个动点.
求圆C的标准方程;
当圆C上存在点Q,使
,求实数m的取值范围;
当
时,过P作直线PA,PB与圆C分别交于异于点P的点A,B两点,且
求证:直线AB恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c79524ae8e494739dbcc5097a0f7c78a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45fb58388a2af941d6658d345829c198.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fef9380b394a4bd829c83a5a5b4c859.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50188630604c9019e00e79b21f32b20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13364e4af8eb2ed915fa0f1caef47dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc304a55feec5d8312d3082f1bb91a23.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/671e0271ef5d6f9784178b28d7d60265.png)
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2018-12-11更新
|
1293次组卷
|
3卷引用:【市级联考】江苏省苏州市常熟市2018-2019学年高二(上)期中数学试卷
【市级联考】江苏省苏州市常熟市2018-2019学年高二(上)期中数学试卷(已下线)第02练 圆与方程-2022年【寒假分层作业】高二数学(苏教版2019选择性必修第一册)河南省洛阳市洛宁县第一高级中学2022-2023学年高二上学期11月月考数学试题
2 . 已知点R为曲线
上任意一点,定点
满足
,过点
分别作斜率为
,
的曲线
的动弦AB,CD,设P,Q分别为线段AB,CD的中点.
求曲线的方程;
当线段AB长度最小时,求
;
若
,求证直线PQ恒过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0103772593e637b3c9adf736e92751ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4d535d53fb78e9354a21a2c09593b3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4e5df6f119904492064df4a63d875ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/731f980ccb6f902d460d0ea2920bfe2c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cb9ad1e34877b0db02d0219332b0f7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f375dc5addedc5f9fbb72d566939c14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4bb89a362c1faf4d0c306eabbb59710.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80036fbb56747a7a63faed9cee348d9d.png)
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名校
3 . 已知过点A(0,4),且斜率为
的直线与圆C:
,相交于不同两点M、N.
(1)求实数
的取值范围;
(2)求证:
为定值;
(3)若O为坐标原点,问是否存在以MN为直径的圆恰过点O,若存在则求
的值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ab821096dca880730ed3cadc2497a98.png)
(1)求实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3c34414e65788c8605c35890188248c.png)
(3)若O为坐标原点,问是否存在以MN为直径的圆恰过点O,若存在则求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2018-12-02更新
|
1485次组卷
|
5卷引用:【全国百强校】广东省汕头市金山中学2018-2019学年高二上学期期中考试 数学
【全国百强校】广东省汕头市金山中学2018-2019学年高二上学期期中考试 数学浙江省舟山市2018-2019学年高二上学期期末数学试题(已下线)专题08 《圆与方程》中的解压题压轴题(2)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)广东省广州西关外语学校与广州理工实验学校联盟2022-2023学年高二上学期期中数学试题广东省揭阳市普宁市兴文中学2023-2024学年高二上学期期中数学试题
4 . 已知直线
与圆
相交于
两点,点
,且
,若
,则实数
的取值范围是__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3016baf1a9ce777f16ea9ce469b2510.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c62a5bc2ddd8b57ed3ab0e3adc507d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bda168b06cad171bf06d1251897622b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ada25f76504c3fd1226da43c94cb4277.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dfb53b8cfebf749bf4c5d70a8b0cc7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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2018-10-26更新
|
1934次组卷
|
2卷引用:【省级联考】四川省高2019届高三第一次诊断性测试(理科)数学
名校
解题方法
5 . 已知直线l:
,半径为4的圆C与直线l相切,圆心C在x轴上且在直线l的右上方.
(1)求圆C的方程;
(2)过点M (2,0)的直线与圆C交于A,B两点(A在x轴上方),问在x轴正半轴上是否存在定点N,使得x轴平分∠ANB?若存在,请求出点N的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45eaae310afe86d8dbdd9079328cf5c3.png)
(1)求圆C的方程;
(2)过点M (2,0)的直线与圆C交于A,B两点(A在x轴上方),问在x轴正半轴上是否存在定点N,使得x轴平分∠ANB?若存在,请求出点N的坐标;若不存在,请说明理由.
您最近一年使用:0次
2018-07-17更新
|
837次组卷
|
2卷引用:【全国百强校】甘肃省兰州第一中学2017-2018学年高二下学期期末考试数学(文)试题
解题方法
6 . 如图在平面直角坐标系xOy中,圆C的方程为
,且圆C与y轴交于M,N两点(点N在点M的上方),直线
与圆C交于A,B两点.
(1)若
,求实数k的值.
(2)设直线AM,直线BN的斜率分别为
,若存在常数
使得
恒成立?若存在,求出a的值.若不存在请说明理由.
(3)若直线AM与直线BN相较于点P,求证点P在一条定直线上.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/396a6ca534c84fc0ab3dc4589fd6157a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c0fe4411fa2e1f2cd598511c17e1bd28.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ff65d41af55dc0e19f7109b96f46a4f.png)
(2)设直线AM,直线BN的斜率分别为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80861c13bb2d470a2953bebc5e3ea044.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4887473a8091e1ef53a169cc9f211e3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ec5c22e1af8746f802946463f39aab2.png)
(3)若直线AM与直线BN相较于点P,求证点P在一条定直线上.
![](https://img.xkw.com/dksih/QBM/2018/7/1/1979222041640960/1981094176514048/STEM/579b3aaf2f8a4f4b8220c82f611c4afa.png?resizew=210)
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7 . 设
是直线
上一点,
是圆
:
上不同的两点,若圆心
是
的重心,则
面积的最大值为__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c966320d637cab491c67425ef1338966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb09e67db6ca9d52c881dcf279ea58c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc3919b5000f9af77ddb77a62bee9c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecc3919b5000f9af77ddb77a62bee9c9.png)
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8 . 已知圆
的方程
.
(1)若点
在圆
的内部,求
的取值范围;
(2)若当
时,
①设
为圆
上的一个动点,求
的最值;
②问是否存在斜率是1的直线
,使
被圆
截得的弦
,以
为直径的圆经过原点,若存在,写出直线
的方程;若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b6e91f5fe568f2df0a2b1255fb8b8fc.png)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2dc6053a01d4152214bf165a237f57cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/711b21672fd907c5c92fee1d649e7003.png)
①设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6bcc89a085b0c46645858581cc48aa29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/449459ad9c5f3a2dce411b722dde995f.png)
②问是否存在斜率是1的直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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9 . 点
到
的距离是点
到
的距离的
倍.
(1)求点
的轨迹方程;
(2)点
与点
关于点
对称,点
,求
的最大值和最小值;
(3)若过
的直线从左向右依次交第(2)问中
的轨迹于不同两点
、
,
,判断
的取值范围并证明.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f55d12701014cf53071093e8739d089b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fad20e2bc6576fc461419f8f138d26e7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df49179dbfbc8e207aa92fd72060fba1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fb348378dcf32cc9a54f81650a9f790.png)
(3)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b9d9e33a62c87229fc3de505c06e173.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
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