解题方法
1 . 已知圆
内有一点
,过点
的直线
与圆
交于
两点,过
分别作圆
的切线
,且
相交于点
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9deb20b57fe0b94ca8520b55298d6c4a.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/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
A.当![]() ![]() ![]() ![]() |
B.点![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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解题方法
2 . 已知圆O的方程为
,与x轴的正半轴交于点N,过点
作直线与圆O交于A、B两点.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/904b633f-5330-4935-bd6d-5ba8bb4a54e6.png?resizew=188)
(1)若坐标原点O到直线AB的距离为1,求直线AB的方程;
(2)如图所示,作一条斜率为-1的直线交圆于R,S两点,连接PS,PR,试问是否存在锐角
,
,使得
为定值?若存在,求出该定值,若不存在,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54329a84abb204cecb237b2bf2ff2bb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/516d6c4c677a9552349b9bf78ec25d87.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/11/15/904b633f-5330-4935-bd6d-5ba8bb4a54e6.png?resizew=188)
(1)若坐标原点O到直线AB的距离为1,求直线AB的方程;
(2)如图所示,作一条斜率为-1的直线交圆于R,S两点,连接PS,PR,试问是否存在锐角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/157c011c410c3a25dd72953187af1506.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c88253c852bbe1c19469ae3900661f9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d1c01fe8e6e31f94fd894588ae27cc0.png)
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解题方法
3 . 已知
的顶点
,
,
.
(1)若直线
过顶点
,且顶点A,
到直线
的距离相等,求直线
的方程;
(2)数学家欧拉于1765年在他的著作《三角形的几何学》中首次提出:三角形的外心、重心、垂心共线,这条直线称为欧拉线.求
的欧拉线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c8c39de4d7d1277da346b51b5bd2499.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/428426e7f2ee0502b555a87a5cef6cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134fc3507b06c25a6cdf06b7ae11f055.png)
(1)若直线
![](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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)数学家欧拉于1765年在他的著作《三角形的几何学》中首次提出:三角形的外心、重心、垂心共线,这条直线称为欧拉线.求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
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4 . 等腰直角三角形ABC的直角顶点B和顶点A都在直线
上,顶点C的坐标是
,直线AC的倾斜角是钝角.
(1)求直线BC,AC在x轴上的截距之和;
(2)平行于AC的直线l与边AB,BC分别交于点D,E,若
的面积等于
,求直线l与两坐标轴围成的三角形的周长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2297db3c14c256b9691fbb8e5bba978.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/71a3619ccbcf65312754a970647014e5.png)
(1)求直线BC,AC在x轴上的截距之和;
(2)平行于AC的直线l与边AB,BC分别交于点D,E,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15514bc735fe4b744672edefe00009c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/533a7b702ada1dd80123e4041271d521.png)
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2023-09-20更新
|
959次组卷
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3卷引用:辽宁省铁岭市昌图县第一高级中学2023-2024学年高二上学期9月月考数学试题
5 . 某市的两条直线公路OM,ON所围成的角形区域内有一村庄
,该市为响应党中央的乡村振兴战略,拟过村庄
修建一条公路,使之围成一个等腰三角形区域
.在区域
内建设高效生态农业示范带,促进本地农村经济发展.现利用无人机在空中测得
到公路OM,ON的距离均为10千米,
,且
.设计人员方便规划计算,在图纸上以
为坐标原点,以直线
为
轴建立如图所示平面直角坐标系
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/fdf24d4a-2633-4576-888b-38dd704299ff.png?resizew=211)
(1)求点
的坐标;
(2)求出公路
的长度及该示范带的总面积.
![](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/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb802b0cd77d772dceff0d9ff6c879ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a84261efd0ff6fafdc55cd446c1a5f68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ebe6a6476bc99d568e2844d32fee8d1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/25/fdf24d4a-2633-4576-888b-38dd704299ff.png?resizew=211)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)求出公路
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
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解题方法
6 . 已知圆
:
,
为圆
上任意一点,![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c397129dacf0871ab2db37e60560f4b9.png)
(1)求
中点
的轨迹方程.
(2)若经过
的直线
与
的轨迹相交于
,在下列条件中选一个,求
的面积.
条件①:直线
斜率为
;②原点
到直线
的距离为
.
![](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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c397129dacf0871ab2db37e60560f4b9.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b83beedb3438153e6f728545fe3e03.png)
条件①:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/56d266a04f3dc7483eddbc26c5e487db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afd3f14f202cd26f36711eefcdc03103.png)
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2023-02-22更新
|
245次组卷
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3卷引用:江西省九校2022-2023学年高二下学期开学联考数学试题
7 . 已知圆
,直线
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79382ba44ba669b5d43fdd5427adf16c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91c432d6472b8410ff5901cdfc5dedbe.png)
A.存在实数m使得圆上的点到直线![]() |
B.存在实数m使得圆上的点到直线![]() |
C.存在实数m使得圆上的点到直线![]() |
D.存在实数m使得圆上的点到直线![]() |
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8 . 已知直线l在x轴,y轴上的截距分别为1,
,O是坐标原点,则下列结论中正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
A.直线l的方程为![]() |
B.过点O且与直线l平行的直线方程为![]() |
C.若点![]() ![]() ![]() |
D.点O关于直线l对称的点为![]() |
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2022-12-22更新
|
994次组卷
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7卷引用:第二章 直线和圆的方程 讲核心02
第二章 直线和圆的方程 讲核心02山东省济宁市邹城市2022-2023学年高二上学期期末数学试题山东省济南第一中学2023-2024学年高二上学期10月月考数学试题广东省2022-2023学年高二上学期12月质量检测联考数学试题山东省2022-2023学年高二上学期12月质量检测联合调考数学试题(已下线)专题01 直线的方程8种常见考法归类(1)(已下线)高二数学开学摸底考01(新高考地区)-2023-2024学年高中下学期开学摸底考试卷
名校
解题方法
9 . 已知圆
,定点
.
(1)过点
作圆
的切线,切点是A,若线段
长为
,求圆
的标准方程;
(2)过点
且斜率为1的直线
,若圆
上有且仅有4个点到
的距离为1,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd06dbe851fd8c6a53e275a41603c8a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f6c19987f273b62f5bbe6554b9efe5.png)
(1)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b66a5b7813e902306477f91f9f4084cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce0249a3ff99c083fa4421877549db1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过点
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2022-11-28更新
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828次组卷
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5卷引用:湖北省襄阳市老河口市第一中学2022-2023学年高二上学期元月月考数学试题
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10 . 一曲线族的包络线(Envelope)是这样的曲线:该曲线不包含于曲线族中,但过该曲线上的每一点,都有曲线族中的一条曲线与它在这一点处相切,若圆
:
是直线族
的包络线,则
,
满足的关系式为___________ ;若曲线
是直线族
的包络线,则
的长为___________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7fa04c1675d6531d99e1150683e5167.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dc9b5e5e1348582fca399b981507629.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2022-05-07更新
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4卷引用:福建省厦门第一中学2023届高三一模数学试题