2021高二上·全国·专题练习
1 . 已知圆
,圆
.
(1)求过点
且与圆
相切的直线的方程;
(2)若与
轴不垂直的直线
交
于
,
两点,交
于
,
两点,且
,求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/708a970b369c840020897e9e40f87d7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33bc376c55ee0c0f8f20d984ef568525.png)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e31fd623eb58b8c0c134b99cb7bd83ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c88e6641854d796ef27e581c33e366c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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名校
2 . 如图,圆
,圆
(
),点
,
,
为圆
上异于点P的两点.若直线
,
与圆
都相切,求证:
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853314930581504/2856806218350592/STEM/c96f9733-2a53-4f14-96f7-13d906244b93.png?resizew=204)
(1)直线
,
的斜率之积为1;
(2)直线
的斜率为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc913bc204342a3c2e9d80d13078fb8c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc24e2d9bcc823abb47d63f98fa6866a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6ebd85aab017840b3f2a7668f403590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c76b94fa972f92861f2fb70bed2ff9cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://img.xkw.com/dksih/QBM/2021/11/17/2853314930581504/2856806218350592/STEM/c96f9733-2a53-4f14-96f7-13d906244b93.png?resizew=204)
(1)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2021-11-22更新
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370次组卷
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5卷引用:浙江省宁波市金兰教育合作组织2021-2022学年高二上学期期中联考数学试题
浙江省宁波市金兰教育合作组织2021-2022学年高二上学期期中联考数学试题江苏省常州市第二中学2022-2023学年高二上学期10月阶段调研数学试题(已下线)第二章 平面解析几何之直线和圆的方程(A卷·知识通关练)(3)(已下线)高二上学期期中【压轴60题考点专练】(选修一全部内容)-2022-2023学年高二数学考试满分全攻略(人教A版2019选修第一册)(已下线)专题02 期中真题精选(压轴93题10类考点专练)(2)
名校
解题方法
3 . 如图:已知A,
是圆
:
与
轴的交点,
为直线
:
上的动点.
![](https://img.xkw.com/dksih/QBM/2021/10/16/2830810328088576/2832129710915584/STEM/97367d17f5dc4dd7ae2e7d4c7708da69.png?resizew=240)
(1)判断直线
与圆
的位置关系,并说明理由;
(2)过点
作圆
的切线,切点为
,
,当
最小时,求直线
的方程;
(3)
,
与圆的另一个交点分别为
,
.求证:直线
过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://img.xkw.com/dksih/QBM/2021/10/16/2830810328088576/2832129710915584/STEM/97367d17f5dc4dd7ae2e7d4c7708da69.png?resizew=240)
(1)判断直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bad3e78e5095b12eb4d5b19880bdd806.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/e1c1270c110ad3bb7e6a252deda48c8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
(3)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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4 . 已知曲线
.从点
向曲线
引斜率为
的切线
,切点为
.
(1)求切点
坐标和切点
的坐标;
(2)已知
在
上是递减的,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9003aa4b018237cb072037fb5c601295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fe413b12ffabfb252121aa2eaa31017.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc31dcdb99754fc452ff2b92a2fb8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32b6db56d3af870687872b9b0ec93821.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c7c5e7bd6bac51402ffa04b4144ec78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1582e020ff2bc37a3afc329583ef0ce5.png)
(1)求切点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf83e20035c3afd6d26ebfd53d768a70.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8aed435445650d8f895db250da2ba8ef.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15144429d33c518bfbb1aec4e8fb1afd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/627c07e6238e8a72112a81af7c351263.png)
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2021-08-24更新
|
160次组卷
|
3卷引用:江西科技学院附属中学2020-2021学年高一下学期期末数学(文)试题
江西科技学院附属中学2020-2021学年高一下学期期末数学(文)试题(已下线)试卷15(第1章-5.1导数的概念)-2021-2022学年高二数学易错题、精典题滚动训练(苏教版2019选择性必修第一册)内蒙古赤峰实验中学、桥北四中2022-2023学年高三下学期大联考数学试题(文科)
解题方法
5 . 如图,已知点
,圆
:
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/1a9042b7-b417-4817-b8b6-1427426abd0c.png?resizew=167)
(1)求过点
且与圆
相切的直线方程;
(2)设圆
与
轴的正半轴的交点是
,斜率为
的直线
过点
,且与圆
交于不同的两点
.
①设直线
的斜率分别是
,求证:
为定值;
②设
的中点为
,点
,当
,且
为整数时,求以
为直径的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/497911bc462170183e81d95bd509b70b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/10/31/1a9042b7-b417-4817-b8b6-1427426abd0c.png?resizew=167)
(1)求过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(2)设圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/01c74a907dda6bb7d9d56d009d9df253.png)
①设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92ca520748c8b8d3878fb112a89ada7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90963760acac7bfad3ae03088c6c80b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b69e3f7ddd51215d00661c09cd900d60.png)
②设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16f36374ce95a4945d0e58264c2b271f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f637d8983f1139258cd0742c60d833e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2021-01-09更新
|
196次组卷
|
3卷引用:安徽省合肥市肥东县高级中学2020-2021学年高三上学期第三次月考数学(理)试题
6 . 已知圆
:
,直线
过定点
.
(1)若
与圆相切,求
的方程;
(2)若
与圆相交于
两点,
线段中点为
,又
与
:
交点为
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e92c9e1ee8f394c2fddc0a22985b95c0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0accaaa66de4dfd9ed8257fa942c2cff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ecdc7bdc6448ef9a13c59fdce1b9bb57.png)
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解题方法
7 . 阿波罗尼斯(约公元前262-190年)证明过这样一个命题:平面内到两定点距离之比为常数
(
且
)的点的轨迹是圆,后人将这个圆称为阿氏圆.已知动点
到点
与点
的距离之比为2,记动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)过点
作曲线
的切线,求切线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f0d68648b10fce54dfc19c5ee60086d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04c525393775354325cbf7839366ca50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0929421a6188c3122442866b0b85a5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf90f8358fa8cd9bc8c99ea48d9ae1a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2020-12-04更新
|
577次组卷
|
3卷引用:安徽省合肥市第十一中学2020-2021学年高二上学期期中数学(文)试题
名校
解题方法
8 . 已知圆
,点P为椭圆
上一点,A,B分别是椭圆C的左右顶点.
(1)若过P点的直线与圆O切于点Q(Q位于第一象限),求使得
面积最大值时的直线PQ的方程;
(2)若直线AP,BP与y轴的交点分别为E,F,以EF为直径的圆与圆O交于点M,求证:直线PM平行于x轴.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52b33328faae2d2d4921900e97424de5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69daca955a565fa537347dd0d93783f.png)
(1)若过P点的直线与圆O切于点Q(Q位于第一象限),求使得
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
(2)若直线AP,BP与y轴的交点分别为E,F,以EF为直径的圆与圆O交于点M,求证:直线PM平行于x轴.
您最近一年使用:0次
2020-08-14更新
|
293次组卷
|
3卷引用:安徽省合肥市第一中学2020届高三下学期最后一卷数学(理)试题
安徽省合肥市第一中学2020届高三下学期最后一卷数学(理)试题(已下线)专题2.6 直线与圆锥曲线的位置关系(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)专题2.7 平面解析几何(B卷提升篇)-2020-2021学年高二数学选择性必修第一册同步单元AB卷(新教材人教B版)
9 . 在平面直角坐标系xOy中,已知圆
与x轴的正负半轴的交点分别是M,N.
(1)已知点
,直线l过点Q与圆O相切,求直线l的方程;
(2)已知点P在直线:
上,直线PM,PN与圆的另一个交点分别为E,F.
①若
,求直线EF的方程;
②求证:直线EF过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
(1)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/32bfddb0c7e57d0b4d9b38d35ee0eb1b.png)
(2)已知点P在直线:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383407840c52dc7878e113e3393e9780.png)
②求证:直线EF过定点.
您最近一年使用:0次
10 . 圆
,点
为直线
上一动点,过点
引圆
的两条切线,切点分别为
,
.
![](https://img.xkw.com/dksih/QBM/2020/9/23/2555891096748032/2555948428902400/STEM/7f624f31aa8a45d1a56837e270fc940f.png?resizew=230)
(1)若点
的坐标为
,求直线
、
的方程;
(2)求证:直线
恒过定点
,并求出该定点
的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061af1c7a4480004221e253d813efe07.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://img.xkw.com/dksih/QBM/2020/9/23/2555891096748032/2555948428902400/STEM/7f624f31aa8a45d1a56837e270fc940f.png?resizew=230)
(1)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c272307fe2fd794353b2ff8fd5f4580f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
(2)求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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