名校
解题方法
1 . 已知
为坐标原点,抛物线
上一点
到抛物线焦点的距离为
,若过点
的直线
与抛物线
交于
,
两点.
(1)证明:
;
(2)若
与坐标轴不平行,且
关于
轴的对称点为
,圆
,证明:直线
恒与圆
相交.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24b3e9aec13bb6f6efe540488ccb6eee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39e238778c3b27483b4d92282b2fcfc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4b8503f4706b8321e4e79a87eadea84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)证明:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3825ccc273ef9a672a606432d165b866.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3761b9d72109ee259e9fec919ebf098c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
您最近一年使用:0次
2023-06-10更新
|
632次组卷
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5卷引用:河南省信阳高级中学2023届高三下学期3月测试(二)理科数学试题
河南省信阳高级中学2023届高三下学期3月测试(二)理科数学试题湖南省长郡、雅礼、一中、附中联合编审名校卷2023届高三下学期月考八文科数学试题(全国卷)(已下线)第05讲 3.3.1抛物线及其标准方程(8类热点题型讲练)-【帮课堂】2023-2024学年高二数学同步学与练(人教A版2019选择性必修第一册)(已下线)重难专攻(十一)?圆锥曲线中的证明,探究性问题(B素养提升卷)(已下线)第八章 平面解析几何(测试)
2 . 已知直线
和圆
.
(1)求证:对任意实数
,直线
和圆
总有两个不同的交点;
(2)设直线
和圆
交于
,
两点.
①若
,求
的倾斜角;
②求弦
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8cdff752dae5a7c374df8867b604dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40e4c065f79e3c13b805efd8a57dd33a.png)
(1)求证:对任意实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ce673a587696689e3b9d6cefecf891b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
②求弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
名校
3 . 已知圆
:
.
(1)求圆
的圆心坐标及半径;
(2)设直线
:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b6e4a25a8896f90bc3c249954bd3d4.png)
①求证:直线
与圆
恒相交;
②若直线
与圆
交于
,
两点,弦
的中点为
,求点
的轨迹方程,并说明它是什么曲线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f46bd6985253f993dc2d1c12b801dc2.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40b6e4a25a8896f90bc3c249954bd3d4.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
②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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](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/ac047e91852b91af639feec23a9598b2.png)
您最近一年使用:0次
2023-05-30更新
|
450次组卷
|
11卷引用:河南省南阳市镇平县第一高级中学2022-2023学年高二下学期5月月考数学试题
河南省南阳市镇平县第一高级中学2022-2023学年高二下学期5月月考数学试题福建省2020-2021学年高二6月普通高中学业水平合格性考试数学试题(已下线)第2章 圆与方程综合测试-【暑假自学课】2022年新高二数学暑假精品课(苏教版2019选择性必修第一册)(已下线)第2章 圆与方程(A卷·知识通关练)(1)云南省大理州鹤庆县第三中学2022-2023学年高二上学期11月月考数学复习题试题(已下线)专题2.9 直线与圆的方程大题专项训练(30道)-2023-2024学年高二数学举一反三系列(人教A版2019选择性必修第一册)(已下线)第11讲 第二章 直线和圆的方程 章末总结(3)(已下线)第1课时 课后 圆的标准方程(已下线)第08讲 圆的方程(3大考点九种解题方法)(2)(已下线)第2章 圆与方程章末题型归纳总结(1)湖南省长沙市长郡湘府中学2022-2023学年高二上学期第一次阶段练习数学试题
解题方法
4 . 已知直线
,
,
,动点
满足
,动点
的轨迹为曲线
.
(1)求曲线
的方程;
(2)证明:直线
与曲线
总有两个交点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c36e68e4e779e15ca1b0200a75d84e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ceec39aaaccbeaac9a4a5bdbb0f0e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4bc333cee094e9dd8f1f3ff86adc95f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab34ce6cee0673ab0d37b660d57bc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2023-09-26更新
|
663次组卷
|
2卷引用:河南省南阳市宛城区2022-2023学年高二上学期第二次月考数学试题
解题方法
5 . 已知圆C:
与直线l:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45af4fa45634408f1cb2e44aeda628a.png)
(1)证明:直线
和圆
恒有两个交点;
(2)若直线
和圆
交于
两点,求
的最小值及此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a32c27759b330c663dca1db376d102e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e45af4fa45634408f1cb2e44aeda628a.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2022-11-22更新
|
176次组卷
|
3卷引用:河南省开封市立洋外国语学校2022-2023学年高二上学期第二次月考数学试题
名校
解题方法
6 . 已知O为坐标原点,C为反比例函数
上的动点,以点C为圆心,|OC|为半径的圆交x轴于O,A两点,交y轴于O,B两点.
(1)求证:△OAB的面积与点C的位置无关.
(2)若直线2x+y-4=0与圆C交于M,N两点,且△OMN为等腰三角形且|OM|=|ON|,求此时圆C的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef854dfcbba9b7dedc1bc52f6332b011.png)
(1)求证:△OAB的面积与点C的位置无关.
(2)若直线2x+y-4=0与圆C交于M,N两点,且△OMN为等腰三角形且|OM|=|ON|,求此时圆C的方程.
您最近一年使用:0次
2022-03-24更新
|
111次组卷
|
2卷引用:河南省濮阳市范县第一中学2021-2022学年高二上学期第二次月考检测数学试题
2022高三·全国·专题练习
7 . 已知直线l:2mx-y-8m-3=0和圆C:x2+y2-6x+12y+20=0.
(1)m∈R时,证明l与C总相交;
(2)m取何值时,l被C截得的弦长最短?求此弦长.
(1)m∈R时,证明l与C总相交;
(2)m取何值时,l被C截得的弦长最短?求此弦长.
您最近一年使用:0次
2021-10-08更新
|
1060次组卷
|
8卷引用:河南省焦作市温县第一高级中学2021-2022学年高二上学期10月月考数学(理)试题
河南省焦作市温县第一高级中学2021-2022学年高二上学期10月月考数学(理)试题(已下线)专题12 直线和圆的方程-备战2022年高考数学一轮复习核心知识全覆盖(新高考地区专用)江西省宜春市上高二中2021-2022学年高二上学期10月月考数学(理)试题浙江省丽水外国语实验学校2020-2021学年高二上学期第一次段考数学试题江西省宜春市上高二中2021-2022学年高二上学期第一次月考数学(理)试题上海市嘉定区第二中学2021-2022学年高二上学期期末数学试题(已下线)第十四课时 课中 第二章 章末复习1.2.3直线与圆的位置关系(习题) -2021-2022学年高二上学期数学北师大版(2019)选择性必修第一册
名校
解题方法
8 . 已知圆
,直线
.
(1)求证:对任意的
,直线
与圆
恒有两个交点;
(2)设
与圆
相交于
两点,求线段
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e948b27f4756cb8ad3cbbbaf13e1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3445947fa34dd409a1354786e6c4a579.png)
(1)求证:对任意的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2725a89d93c791f7a0098f4964587905.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b2d2b82cd298e88b2e8904738ba37c.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27b2d2b82cd298e88b2e8904738ba37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/2020/12/16/2615390022164480/2615662107066368/STEM/9c487c0525314effaed33ef2a3883418.png?resizew=189)
您最近一年使用:0次
2020-12-16更新
|
402次组卷
|
7卷引用:河南省信阳高级中学2020-2021学年高一下学期开学考试数学(理)试题
9 . 已知圆
:
关于直线
对称且过点
和
,直线
的方程为:
.
(1)证明:直线
与圆
相交;
(2)记直线
与圆
的两个交点为
,
.
①若弦长
,求实数
的值;
②求
面积的最大值及
面积的最大时
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e885d3743ae3d9f0fbd740b75f900083.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ec89d17a1b8f7961e2f1f27c2d50685.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0fe3f68cbbcc907caab5083d08df301.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cc46f09a8c079e2916af98bb2f96f84.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc0b7ecccdda6623f2a49e6e05cd7c4c.png)
(1)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)记直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
①若弦长
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/077c956ac0eb05cf120e14f17413dfa2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0faed94a64b2dcfc6801b4fca0f16675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
名校
解题方法
10 . 已知椭圆
的左、右焦点
,
,
是椭圆
上的动点,且
面积的最大值为
.
(1)求椭圆
的方程及离心率;
(2)若
是椭圆
的左、右顶点,直线
与椭圆在点
处的切线交于点
,当点
在椭圆上运动时,求证:以
为直径的圆与直线
恒相切.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.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/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
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