名校
1 . 已知椭圆
的左、右焦点分别为
、
,过椭圆的右焦点
作一条直线
交椭圆于点
、
.则
内切圆面积的最大值是_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6cae00bdc6f8b564b6b15b32572c848b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/35eb8a895a6122917c531afea1a83284.png)
您最近一年使用:0次
2017-05-27更新
|
2096次组卷
|
11卷引用:2007年全国高中数学联赛吉林赛区预赛试题
(已下线)2007年全国高中数学联赛吉林赛区预赛试题2019年全国高中数学联赛甘肃省预赛福建省泉州市2017届高三高考考前适应性模拟(二)理数试题福建省泉州市2017届高三高考考前适应性模拟卷(二) 数学(文)试题2019届四川省双流中学高三下学期第三次模拟考试数学(理)试题人教B版(2019) 选择性必修第一册 过关斩将 第二章 平面解析几何 2.8 直线与圆锥曲线的位置关系重庆市西南大学附属中学2020-2021学年高二下学期第三次月考数学试题苏教版(2019) 选修第一册 一蹴而就 模块整合(已下线)专题06 《圆锥曲线与方程》中的压轴题(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) (已下线)专题28 《圆锥曲线与方程》中的内接内切问题-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) (已下线)2022年高考考前20天终极冲刺攻略(三)【理科数学】(5月29日)
2 . 已知抛物线
:
和动直线
:
(
,
是参变量,且
,
)相交于
,
两点,直角坐标系原点为
,记直线
,
的斜率分别为
,
,若
恒成立,则当
变化时直线
恒经过的定点为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c15fb18163df0690365a0d2e7ee88f5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b03b011f69dfc5262a3d82f64676739b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6ff82ebdfad5e7de1c7487b0b817a7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a53e311ee0b5085e7e5a45c606daa5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be8fe7e29e32d3d529957d62fe37350e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7ac42906a2f4da22b764e76fef60c68.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39864314058fe5aa03d9b6ff92466924.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
3 . 已知抛物线
内一定点
,过点
分别作斜率为
,
的两条直线
、
,交抛物线于
、
和
、
四点,设
、
分别为线段
和
的中点.
(1)当
且
时,求
的面积的最小值;
(2)若
(
为常数,且
),证明:直线
过定点,并求出定点坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3764ba3aa0a241787f4661026bb14053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcc5dd4d07e2098d8d1b731f2622867f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd09fb9482124fd35f19b86894648f4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/257beb71337358f5ccc57219d9153666.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c1e860e7d762c206d296cffbdd2786e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fbecca12ee62538020483fd55a2109.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
您最近一年使用:0次
名校
解题方法
4 . 已知中心在原点的椭圆
的两焦点分别为双曲线
的顶点,直线
与椭圆
交于
、
两点,且
,点
是椭圆
上异于
、
的任意一点,直线
外的点
满足
,
.
(1)求点
的轨迹方程;
(2)试确定点
的坐标,使得
的面积最大,并求出最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ea74737939c0f94c91229a7098f36ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d373ef598634c09fd59744f8411d4037.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/b0d22b413e83596b011dd23e25d4090f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad492faa37d468027765399b64574439.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0e65c1d8e47c4698ced909db38ec2c.png)
(1)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
(2)试确定点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed283a253b61df01f2a1cdc0cd8003f3.png)
您最近一年使用:0次
2017-04-01更新
|
805次组卷
|
2卷引用:2017届广西陆川县中学高三下学期知识竞赛理数试卷
名校
解题方法
5 . 已知
是抛物线
上一点,经过点
的直线
与抛物线
交于
两点(不同于点
),直线
分别交直线
于点
.
(1)求抛物线方程及其焦点坐标,准线方程;
(2)若
,求直线
的方程;
(3)已知
为原点,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05a71e8f88d276a810aa245ed5d0cb39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7df40ba57bb5819b4aaa38d514500052.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d8ac8fa800c00933279f2b20e5034438.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba57445efa8ad1501d049e551f34a158.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/639c3d2ff5ee566fcc1b69c65712a661.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
(1)求抛物线方程及其焦点坐标,准线方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/637223cc3a9bf9e3ea598dc04a28f6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
(3)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27935c1ef4df2d52ac697678a3c8f39d.png)
您最近一年使用:0次
2017-03-03更新
|
1230次组卷
|
2卷引用:2016-2017学年安徽省阜阳市临泉县第一中学高二1月学科竞赛数学(理)试卷
2014·吉林长春·一模
解题方法
6 . 如图,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的左焦点为
,过点
的直线交椭圆于
两点.
的最大值是
,
的最小值是
,满足
.
(1) 求该椭圆的离心率;
(2) 设线段
的中点为
,
的垂直平分线与
轴和
轴分别交于
两点,
是坐标原点.记
的面积为
,
的面积为
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f82eb4ba631d0f50d848aa6e576b379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b52ef609c3dc3aed1b282c3761cedb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/390673ed1f32c7ced6ed818f7f683285.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf1a55baa03a144da10e277aaf81c3a4.png)
(1) 求该椭圆的离心率;
(2) 设线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91e1e4115d78e625e9e0f47cdade3286.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/77399f3111e5580fda53bd9118630cf0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/90790ea39f5c5b578f0dbd8b14bd6617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdbdf7e9f3dd474fd0a6ebbc40fe6635.png)
![](https://img.xkw.com/dksih/QBM/2017/2/8/1625058740813824/1625058741518336/STEM/2026fe1144aa406984a79eb0765dfc98.png?resizew=216)
您最近一年使用:0次
2017-02-16更新
|
1110次组卷
|
7卷引用:2015年全国高中数学联赛黑龙江赛区预赛试题
2015年全国高中数学联赛黑龙江赛区预赛试题(已下线)2015届吉林省长春市新高三起点调研考试理科数学试卷2017届湖南长沙一中高三文月考五数学试卷(已下线)黄金30题系列 高三年级数学(文) 大题好拿分【基础版】湖南省怀化市2023届高三二模数学试题专题20平面解析几何(解答题)(已下线)专题15 圆锥曲线综合
7 . 已知
为抛物线
上的两个动点,点
在第一象限,点
在第四象限,
分别过点
且与抛物线
相切,
为
的交点.
(Ⅰ)若直线
过抛物线
的焦点
,求证动点
在一条定直线上,并求此直线方程;
(Ⅱ)设
为直线
与直线
的交点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bb4dd4670828f75bc573b52cdd02e1d.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/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
(Ⅰ)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(Ⅱ)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f23d29646155e27b172ecdf263e2d702.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/554ee80237c89f3aa26c94aaca374f4d.png)
您最近一年使用:0次
2010·湖南长沙·一模
名校
解题方法
8 . 已知中心在原点,焦点在
轴上的椭圆C的离心率为
,且经过点
.
(1)求椭圆C的方程;
(2)是否存在过点
的直线
与椭圆
相交于不同的两点
,
,满足
?若存在,求出直线
的方程;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e67baac84cf5c95d06d50c36cab7c68.png)
(1)求椭圆C的方程;
(2)是否存在过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4754fbe523ca63eba3810a3f88f37df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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18卷引用:2019年河南省郑州市高二数学选拔赛
2019年河南省郑州市高二数学选拔赛(已下线)湖南省长沙市一中2010届高三第一次模拟考试文科数学试题(已下线)2010年北京市朝阳区高三下学期一模数学(文)测试(已下线)2011届甘肃省武威六中高三第一次诊断考试理科数学卷(已下线)2012届山东省高考模拟冲刺卷文科数学(三)(已下线)2011-2012学年湖南省望城一中高二下学期期中理科数学试卷(已下线)2012届山东省鄄城一中高三下学期模拟冲刺考试文科数学试卷2015届吉林省实验中学高三年级第二次模拟考试理科数学试卷2014-2015学年山东省济南第一中学高二下学期期中考试文科数学试卷2015-2016学年江苏省启东中学高二上学期期末考试数学试卷2016届广东省华南师大附中四校高三上期末联考文科数学试卷2016届天津市河东区高考一模考试理科数学试卷陕西省黄陵中学2017届高三(重点班)下学期高考前模拟(一)数学(文)试题福建省永春一中、培元、季延、石光中学四校2018届高三上学期第二次联考数学(文)试题【全国市级联考】吉林省延边州2018届高三高考仿真模拟数学(文科)试题【校级联考】安徽省芜湖市四校2018-2019学年高二上学期期末联考数学(文)试题【全国百强校】天津市耀华中学2017-2018学年高二上学期期末考试数学(文)试题天津市西青区2022-2023学年高二上学期期末数学试题
2010·浙江·一模
名校
9 . 已知中心在原点
,焦点在
轴上,离心率为
的椭圆过点![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c29aaa3bcd09b9280755cd091b35f6.png)
![](https://img.xkw.com/dksih/QBM/2016/1/5/1572416605102080/1572416610746368/STEM/d1df4eec8801405c8b86d736905516a5.png)
(1)求椭圆的方程;
(2)设不过原点
的直线
与该椭圆交于
两点,满足直线
的斜率依次成等比数列,求
面积的取值范围.
![](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/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66c29aaa3bcd09b9280755cd091b35f6.png)
![](https://img.xkw.com/dksih/QBM/2016/1/5/1572416605102080/1572416610746368/STEM/d1df4eec8801405c8b86d736905516a5.png)
(1)求椭圆的方程;
(2)设不过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ce1e07d1031dd1208dca2528f25fb57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a323e19349e16056e60b3e0b2909e43.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c17bcffba755a9cb6e159baf59ebeb62.png)
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9卷引用:2012年全国高中数学联赛辽宁赛区预赛试题
(已下线)2012年全国高中数学联赛辽宁赛区预赛试题(已下线)2011届浙江省高三高考样卷数学理卷(已下线)2014届湖南汝城第一中学、长沙实验中学高三11月联考文数学卷2016届湖南省长沙市雅礼中学高三月考三理科数学试卷2016-2017年河南西平县高级中学高二文12月考数学试卷山西省晋城一中2017--2018学年度高二12月月月考数学文试题宁夏回族自治区银川市兴庆区宁一中2019-2020学年高二上学期期中数学(文)试题2020届湖南省长沙市长郡中学高三第五次月考数学(理)试题黑龙江省大庆实验中学(实验三部)2019-2020学年高二3月月考数学(理)试题
10 . 已知平面上的动点
与点
连线的斜率为
,线段
的中点与原点连线的斜率为
,
(
),动点
的轨迹为
.
(1)求曲线
的方程;
(2)恰好存在唯一一个同时满足以下条件的圆:
①以曲线
的弦
为直径;
②过点
;
③直径
.求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de58da7c75e870900dd21d557843ae29.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4507f38705cf76db17fcf9e1e05ac0a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8ffe24cf9f327aeb241225ab15ab1a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/158daa4c273a257bea0bea596272b92a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e5944d745732dfb63449b38882e3b3f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/289bf40b793f86f5e98fa7ab16724a46.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)恰好存在唯一一个同时满足以下条件的圆:
①以曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
②过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
③直径
![](https://img.xkw.com/dksih/QBM/2015/5/13/1572104088788992/1572104094924800/STEM/dd44bf3c742743f692667708a8689495.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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