名校
解题方法
1 . 已知椭圆
与抛物线
有相同的焦点
,抛物线
的准线交椭圆
于
两点,且
.
(1)求椭圆
与抛物线
的方程;
(2)
为坐标原点,若
为椭圆
上任意一点,以
为圆心,
为半径的圆
与椭圆
的焦点
为圆心,以
为半径的圆
交于
两点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dce4ea1d967255a19f1035ddbbf2aad6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bf92a1ba410263d4f68b7e0432b19aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/236f52e04ddbd7253f44b97c4756ef9c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abd13974aebe38eb2a1d744a01ea5aa5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b454cdb97c408300b50d945f002c2cb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2967337e3fcb228dded64ab0c41a17e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次
2021-05-04更新
|
290次组卷
|
5卷引用:考向39 直线与圆、圆与圆的位置关系-备战2022年高考数学一轮复习考点微专题(新高考地区专用)
(已下线)考向39 直线与圆、圆与圆的位置关系-备战2022年高考数学一轮复习考点微专题(新高考地区专用)陕西省榆林市2020-2021学年高三上学期一模理科数学试题(已下线)专题21 抛物线综合-2020年高考数学母题题源全揭秘(浙江专版)(已下线)押第21题圆锥曲线-备战2021年高考数学临考题号押题(浙江专用)甘肃省张掖市某重点校2023-2024学年高二上学期9月月考数学试题
解题方法
2 . 已知动点
与两个定点
,
的距离的比为
,动点
的轨迹为曲线
.
(1)求
的轨迹方程,并说明其形状;
(2)过直线
上的动点
分别作
的两条切线
,
(
、
为切点),
,
交
于点
,
(ⅰ)证明:直线
过定点,并求该定点坐标;
(ⅱ)是否存在点
,使
的面积最大?若存在,求出点
坐标:若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/19b62194097ac66a5093c57fca2f5b4f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/241ce9bd28046ce9b90f43b391132884.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e55aa0a20848c37c1892c567b2315e04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/24f5d8c61018a62b012a17a50083f51d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902f97913e1af1e6c793f7edfe6b2114.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d42f05b013e4b7166cbc87c5a83d6a85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2be49c37e30a3ced0364c3e74d8c687.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(ⅰ)证明:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d7b816eca15d4b7d060013df53edd53.png)
(ⅱ)是否存在点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7ad41b36674fd6e90176ee24cdefbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
2021-08-08更新
|
720次组卷
|
4卷引用:第10讲 圆与圆的位置关系(5大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)
(已下线)第10讲 圆与圆的位置关系(5大考点)-2022-2023学年高二数学考试满分全攻略(人教A版2019选择性必修第一册)四川省遂宁市绿然教科院2021-2022学年高二上学期期末联考数学(理)试题湖南省岳阳市2020-2021学年高二下学期期末数学试题(已下线)2.5.2 圆与圆的位置关系(分层作业)(3种题型分类基础练+能力提升练)-【上好课】高二数学同步备课系列(人教A版2019选择性必修第一册)
3 . 已知圆
,圆
,证明圆
与圆
相交,并求圆
与圆
的公共弦所在直线的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0d9aa06aae653c5d9206ceefd7df7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9444c86466e14ecbaf69c7647b7d4835.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2021-02-06更新
|
933次组卷
|
4卷引用:沪教版(2020) 选修第一册 新课改一课一练 期中测试B
解题方法
4 . 已知圆
:
,圆
:
.且圆
上任意一点关于直线
的对称点都在圆
上.
(1)求圆
的方程;
(2)证明圆
和圆
相交,并求两圆公共弦的长度
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d1355d0154d6172c94fd7b17856648e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17302a7b4f322fde48fff8c95a321eff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfab8f6aaf05b1db2db85b60362f3047.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)证明圆
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2020-12-02更新
|
331次组卷
|
4卷引用:沪教版(2020) 选修第一册 领航者 第2章 2.1圆 第4课时 圆与圆的位置关系
沪教版(2020) 选修第一册 领航者 第2章 2.1圆 第4课时 圆与圆的位置关系山西省太原市2020-2021学年高二上学期期中质量监测数学试题(已下线)第2章 圆与方程单元检测卷-2021-2022学年高二数学尖子生同步培优题典(苏教版2019选择性必修第一册)(已下线)2.5 直线与圆、圆与圆的位置关系-2021-2022学年高二数学10分钟课前预习练(人教A版2019选择性必修第一册)
名校
解题方法
5 . 已知圆
与两条坐标轴都相交,且与直线
相切.
(1)求圆
的方程;
(2)若动点
在直线
上,过
引圆
的两条切线
,
,切点分别为
,
,求证:直线
恒过定点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad37cc115251748266cdaeb9fb071208.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc8b515c0b57767af60c121f89277af2.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(2)若动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da322ac8867e8a47c6588601078abf18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](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/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
您最近一年使用:0次
2020-09-04更新
|
532次组卷
|
4卷引用:福建省南安市侨光中学2022-2023学年高二上学期第二次阶段考试(12月)数学试题
6 . 已知圆
经过坐标原点
和点
,且圆心
在直线
上.
(1)求圆
的方程;
(2)设
是圆
的两条切线,其中
为切点.
①若点
在直线
上运动,求证:直线
经过定点;
②若点
在曲线
(其中
)上运动,记直线
与
轴的交点分别为
, 求
面积的最小值.
![](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/f0a44860d62bc01fad8be61e39cf8866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512f4c29ff276b7f35052ad4cc255ab5.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d4a832771ba45d407f31000c8fcf37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
①若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97c6d3c99b7004603ba9ea9c341b8b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16688590aa75a979cc269d934f1bf899.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d4a832771ba45d407f31000c8fcf37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
您最近一年使用:0次
名校
7 . 已知圆
与圆
.
(1)求证两圆相交;
(2)求两圆公共弦所在直线的方程;
(3)求过两圆的交点且圆心在直线
上的圆的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/918e06b55deedf5d11baa3742a3296b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7fa56fa118b343018941be47958637d.png)
(1)求证两圆相交;
(2)求两圆公共弦所在直线的方程;
(3)求过两圆的交点且圆心在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9615fb005e74640174d0f55e4a18476.png)
您最近一年使用:0次
2018-01-12更新
|
1662次组卷
|
4卷引用:河北省邯郸市魏县第五中学2022-2023学年高二上学期第二次月考数学试题
12-13高一上·福建泉州·期末
名校
8 . 已知圆
,直线
,点
在直线
上,过点
作圆
的切线
、
,切点为
、
.
(1)若
,求
点坐标;
(2)若点
的坐标为
,过
作直线与圆
交于
、
两点,当
时,求直线
的方程;
(3)求证:经过
、
、
三点的圆与圆
的公共弦必过定点,并求出定点的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04bc6e1c92d95a19db819486d5f6003a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e34208e402459a84dda851a03ef45d8.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5aae6b928c589af8fff50792d29d16e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25f114df5ceabdb7e5fd3fdad4eaf056.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5e68edcc956f523102e8ed94b1aa98a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(3)求证:经过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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
2016-12-02更新
|
2673次组卷
|
16卷引用:第2章 圆与方程(培优卷)-【满分计划】2022-2023学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)
第2章 圆与方程(培优卷)-【满分计划】2022-2023学年高二数学阶段性复习测试卷(苏教版2019选择性必修第一册)(已下线)2012-2013学年福建南安一中高一上期末考试数学试卷【全国校级联考】福建省福州市八县(市)协作校2016-2017学年高一上学期期末联考数学试题重庆市黔江新华中学校2019-2020学年高二上学期10月月考数学试题2019-2020学年高一上学期期末复习1月第02期(考点15-17)-《新题速递·数学》甘肃省天水一中2019-2020学年高一上学期第三学段(期末)考试数学试题甘肃省武威市古浪三中2019-2020学年高一下学期月考数学试题黑龙江省七台河市勃利县2019-2020学年高一(下)期末数学试题黑龙江省勃利县高级中学2019-2020学年高一下学期期末考试数学试题江西省上高二中2020-2021学年高二上学期第一次月考数学(文)试题(已下线)考点45 直线与圆、圆与圆的位置关系(考点专练)-备战2021年新高考数学一轮复习考点微专题(已下线)对点练51 直线与圆的位置关系-2020-2021年新高考高中数学一轮复习对点练(已下线)第二章 章末检测-2020-2021学年高二数学同步课堂帮帮帮(人教A版2019选择性必修第一册)(已下线)专题11 直线与圆 -备战2021年新高考数学纠错笔记 (已下线)第2章 圆与方程(B卷-提升卷)-2021-2022学年高二数学同步单元AB卷(苏教版2019选择性必修第一册)【学科网名师堂】(已下线)第二章 (综合培优)直线与圆的方程 B卷-【双基双测】2021-2022学年高二数学同步单元AB卷(人教A版2019选择性必修第一册)