2014·江苏徐州·三模
1 . 如图所示,已知A1,A2,B1,B2分别是椭圆C:
(a>b>0)的四个顶点,△A1B1B2的外接圆为圆M,椭圆C过点
.
(1)求椭圆C及圆M的方程;
(2)若点D是圆M劣弧
上一动点(点D异于端点A1,B2),直线B1D分别交线段A1B2,椭圆C于点E,G,直线B2G与A1B1交于点F.
(i)求
的最大值;
(ii)E,F两点的横坐标之和是否为定值?若是,求出该定值;若不是,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f9cae30e954aa12a36d4e1ce145b3b0.png)
(1)求椭圆C及圆M的方程;
(2)若点D是圆M劣弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a10ec63b540f0ee4093a38606ed63ffa.png)
(i)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e07cf2034c6fd6e1a8076e8f5c57cbf.png)
(ii)E,F两点的横坐标之和是否为定值?若是,求出该定值;若不是,说明理由.
![](https://img.xkw.com/dksih/QBM/2014/5/13/1571715011739648/1571715017433088/STEM/1655d50a2c90449b85c2021859bd712a.png?resizew=303)
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名校
2 . 已知椭圆
过点
,且离心率
.
(1)求椭圆方程;
(2)若直线
与椭圆交于不同的两点
,且线段
的垂直平分线过定点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60abe74c6c4ee851937ceea1cffa70c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/964e2ff97122345be34c212a9ee71a76.png)
(1)求椭圆方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b00a552e4e4bbf12ba59bfbea9fa53b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5182b8cf23d443b08db67dda809112ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da265da7dc8e40f22ac9eb76f8b3b4b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d5f06c21b1808cb2b459ea67105bf10d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b61ed9fd6fbfbea7a406c80a7b92df8.png)
![](https://img.xkw.com/dksih/QBM/2018/1/30/1871416843362304/1873655992123392/STEM/ce4afb1839014be4b8046dc3cb54751f.png?resizew=227)
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2018-02-02更新
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6卷引用:江苏省盐城中学2020届高三下学期第一次模拟数学试题
11-12高二上·江苏淮安·期末
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3 . 椭圆
的左、右焦点分别为
,离心率为
,过焦点
且垂直于
轴的直线被椭圆
截得的线段长为
.
(Ⅰ)求椭圆
的方程;
(Ⅱ)点
为椭圆
上一动点,连接
、
,设
的角平分线
交椭圆
的长轴于点
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb1927c60bb332c9ef6c4a18fbf10e90.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0739793f234f8e86adc6177801ae7295.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c94fe48bf7af022ecbbe13833fdcc2c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8649ce18c628d0e03e72cef541f8284f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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12卷引用:2011届江苏省南京金陵中学高三预测卷3数学
(已下线)2011届江苏省南京金陵中学高三预测卷3数学(已下线)2010-2011年江苏省淮安市楚州中学高二上学期期末考试数学试卷(已下线)2012届江苏省扬州中学高三练习数学【市级联考】辽宁省沈阳市2019届高三上学期一模数学(文)试题【市级联考】辽宁省沈阳市2019届高三上学期一模数学(理)试题【市级联考】辽宁省沈阳市2019年高中三年级教学质量监测(一)文科数学试题沈阳市2019年高中三年级教学质量监测(一)理科数学试题【全国百强校】甘肃省兰州市第一中学2019届高三6月最后高考冲刺模拟数学(理)试题山东省2020届普通高等学校招生全国统一考试数学试题模拟卷(二)山东省2020届高三新高考模拟猜想卷(三)数学试题新高考2021届高三考前保温热身模拟卷数学试题(五)宁夏银川一中2022届高三上学期第六次月考数学(理)试题
4 . 已知椭圆
.过点(m,0)作圆
的切线l交椭圆G于A,B两点.
(I)求椭圆G的焦点坐标和离心率;
(II)将
表示为m的函数,并求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f0748ec234ec293d31b395d0549016e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
(I)求椭圆G的焦点坐标和离心率;
(II)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05da40a2d7dab5d6a003906ca19d4749.png)
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|
3237次组卷
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13卷引用:2012届江苏省东海二中高三第三次学情调查数学试卷
(已下线)2012届江苏省东海二中高三第三次学情调查数学试卷2011年普通高中招生考试北京市高考理科数学(已下线)2012届河北省冀州中学高三上学期期中理科数学试卷(已下线)2011-2012学年吉林省长春二中高二上学期期末考试理科数学(已下线)2011—2012学年天津市天津一中高二第一学期期末理科数学试卷2015-2016学年山东省枣庄三中高二上学情调查理科数学卷福建省莆田第九中学2017-2018学年高二上学期期中考试数学(理)试题安徽省滁州市定远县育才学校2019-2020学年高二下学期4月月考数学(文)试题山西省实验中学2020-2021学年高二上学期第三次月考数学(理)试题山西省实验中学2019届高三上学期第四次月考数学试题陕西省西安市长安区第一中学2020-2021学年高二上学期期中数学(文)试题人教B版(2019) 选修第一册 北京名校同步练习册 第二章 平面解析几何初步 2.5椭圆 2.5.2椭圆的几何性质(二)北京名校2023届高三一轮总复习 第7章 解析几何 7.12 直线与圆锥曲线的位置关系(2)
5 . 已知椭圆
:
.
(1)椭圆
的短轴端点分别为
,
(如图),直线
,
分别与椭圆
交于
,
两点,其中点
满足
,且
.
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021151289344/1573021157171200/STEM/8f827f8371ec422eb02fd3855fe81ab1.png?resizew=307)
①证明直线
与
轴交点的位置与
无关;
②若△
面积是△
面积的5倍,求
的值;
(2)若圆
:
.
,
是过点
的两条互相垂直的直线,其中
交圆
于
、
两点,
交椭圆
于另一点
.求△
面积取最大值时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
(1)椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.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/4ec9c2bbf37199b17edb138d49511fa1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baedc4d7e690ab3f7d80d30ba0a9efe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cba0d86458322433a3e4e78ef3915fa3.png)
![](https://img.xkw.com/dksih/QBM/2016/9/14/1573021151289344/1573021157171200/STEM/8f827f8371ec422eb02fd3855fe81ab1.png?resizew=307)
①证明直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
②若△
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f8d4dc8f1c33bfbdadbfb2b8d75cc6e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75445760eb6944d4c380707bc83ab36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)若圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5f5d967ad135991b6075ee45df55643.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e54822a1c8cd1ad8c5b84e1c33ed9bfc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f99b96932484063d4635cf396aa3c3b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
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6 . 如图,在平面直角坐标系xOy中,椭圆
的左,右顶点分别为
·若直线3x+4y+5=0上有且仅有一个点M,便得
.
(1)求椭圆C的标准方程
(2)设圆T的圆心T(0,t)在x轴上方,且圆T经过椭圆C两焦点,点P,Q分别为椭圆C和圆T上的一动点,若
时,PQ取得最大值为
,求实数t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe81ab3794e4a149d6132a4080494619.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5879bb9eef25b9bd4d7eae64834fc95b.png)
(1)求椭圆C的标准方程
(2)设圆T的圆心T(0,t)在x轴上方,且圆T经过椭圆C两焦点,点P,Q分别为椭圆C和圆T上的一动点,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b58d088853885bd6ea454228b8eb57f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/31f8f7e40ba386c0a9675896b52752d6.png)
![](https://img.xkw.com/dksih/QBM/2018/5/28/1955024646635520/1956671213871104/STEM/44dfd620fede4f0baad4952ae27b7031.png?resizew=195)
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2016-12-03更新
|
1639次组卷
|
2卷引用:2015届江苏省淮安市高三第五次模拟考试数学试卷
7 . 如图,过椭圆
的左顶点
和下顶点
且斜率均为
的两直线
分别交椭圆于
,又
交
轴于
,
交
轴于
,且
与
相交于点
.当
时,
是直角三角形.
![](https://img.xkw.com/dksih/QBM/2015/5/11/1572099271368704/1572099277422592/STEM/8a16ca50ccba427dbbd95c8d67fc53cc.png)
(1)求椭圆L的标准方程;
(2)①证明:存在实数
,使得
;
②求|OP|的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c88d9142df6ba8e43c1a93bd04a1362.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2cae50df1c0052f7721173c353f812fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44434b647ec546fe787e2164e0be6cd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39acab3cfb59bfc9591371721ab01d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/367e788c32187ae2cc97aaa24da1d40d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aa65b2cdc271e9a4a9080e067ca31f91.png)
![](https://img.xkw.com/dksih/QBM/2015/5/11/1572099271368704/1572099277422592/STEM/8a16ca50ccba427dbbd95c8d67fc53cc.png)
(1)求椭圆L的标准方程;
(2)①证明:存在实数
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5fffd330dd6b9241659d790bd2a7fb2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82057c0973eb9eb353db9a8c854b78dc.png)
②求|OP|的最小值.
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8 . 如图,在平面直角坐标系
中,椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
的左顶点为
,与
轴平行的直线与椭圆
交于
、
两点,过
、
两点且分别与直线
、
垂直的直线相交于点
.已知椭圆
的离心率为
,右焦点到右准线的距离为
.
![](https://img.xkw.com/dksih/QBM/2015/4/22/1572082488459264/1572082494414848/STEM/a1a89dec24bf43fd94552319013e9232.png)
(1)求椭圆
的标准方程;
(2)证明点
在一条定直线上运动,并求出该直线的方程;
(3)求
面积的最大值.
![](https://img.xkw.com/dksih/QBM/2015/4/22/1572082488459264/1572082494414848/STEM/1523e90332d94fc2b9abd28972f90366.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fdc384aa20e27b9289497e741e35554.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ec56b59d6f2654570c2b5c4fd13a05.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/2a30f3a8b673cc28bd90c50cf1a35281.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.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/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe2c533dbc23a34518f72f3cb14f330.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c98ee8ce2c56dccae6b63b5a9ca022b8.png)
![](https://img.xkw.com/dksih/QBM/2015/4/22/1572082488459264/1572082494414848/STEM/a1a89dec24bf43fd94552319013e9232.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)证明点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(3)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dc0fe7a934cca2a64cfdab0a37112368.png)
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真题
名校
9 . 已知椭圆C:
(
)的焦距为4,其短轴的两个端点与长轴的一个端点构成正三角形.
(1)求椭圆C的标准方程;
(2)设F为椭圆C的左焦点,T为直线
上任意一点,过F作TF的垂线交椭圆C于点P,Q.
(i)证明:OT平分线段PQ(其中O为坐标原点);
(ii)当
最小时,求点T的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9374d3462754e846cbb0f7dd5fd28277.png)
(1)求椭圆C的标准方程;
(2)设F为椭圆C的左焦点,T为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a858da0ca2754da9f1b93e3574d2401.png)
(i)证明:OT平分线段PQ(其中O为坐标原点);
(ii)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1658832f5edbe3c99489e8462ccbaa5.png)
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2016-12-03更新
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17卷引用:江苏省镇江市丹阳高中、镇江一中、镇江中学三校2020届高三下学期5月调研数学试题
江苏省镇江市丹阳高中、镇江一中、镇江中学三校2020届高三下学期5月调研数学试题2015届天津市河西区高三下学期总复习质量调查一理科数学试卷江苏省镇江中学2019-2020学年高二上学期第一次月考数学试题江苏省镇江中学2019-2020学年高二上学期10月月考数学试题陕西省西安市西安中学2024届高三模拟考试(九)数学(理科)试题2014年全国普通高等学校招生统一考试理科数学(四川卷)2014-2015学年重庆市杨家坪中学高二上学期第三次月考理科数学试卷广东省潮州市2019-2020学年高三上学期期末数学(文)试题上海市复兴高级中学2015-2016学年高二上学期期末数学试题广东省罗定第二中学2020届高三上学期期末教学质量检测数学(文科)试题沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第十章 坐标平面上的直线与线性规划高考题选沪教版(上海) 高三年级 新高考辅导与训练 第二部分 走近高考 第十一章 圆锥曲线高考题选(已下线)第42讲 解析几何中的长度之和差积商平方问题-2022年新高考数学二轮专题突破精练(已下线)专题46 盘点圆锥曲线中的最值与范围问题——备战2022年高考数学二轮复习常考点专题突破陕西省安康市白河高级中学实验班2021-2022学年高二上学期期末理科数学试题(已下线)专题07 盘点求最值的六种方法-2(已下线)专题24 解析几何解答题(理科)-1
13-14高二下·浙江嘉兴·期中
名校
解题方法
10 . 如图,椭圆
:
(
)和圆
:
,已知圆
将椭圆
的长轴三等分,椭圆
右焦点到右准线的距离为
,椭圆
的下顶点为
,过坐标原点
且与坐标轴不重合的任意直线
与圆
相交于点
、
.
![](https://img.xkw.com/dksih/QBM/2014/7/2/1571805974052864/1571805980041216/STEM/0bb1e4dd-90cf-41b1-8812-a78e183feb4e.png?resizew=296)
(1)求椭圆
的方程;
(2)若直线
、
分别与椭圆
相交于另一个交点为点
、
.
①求证:直线
经过一定点;
②试问:是否存在以
为圆心,
为半径的圆
,使得直线
和直线
都与圆
相交?若存在,请求出实数
的范围;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef74c4299221a967507c6a179337581a.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/821309f088a175c00dc0f4828334503d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.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/2014/7/2/1571805974052864/1571805980041216/STEM/0bb1e4dd-90cf-41b1-8812-a78e183feb4e.png?resizew=296)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1642eec556eb252de9c1ab7bb5ca90b3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccaee8f228ff24e7c89879bb5b999cf2.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/ac047e91852b91af639feec23a9598b2.png)
①求证:直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/438f34bc8b04e8c494b91306ac6fe352.png)
②试问:是否存在以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b67c623950b5795d5fb4daeb8102a8df.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3084250c16aa160cb58887bcf6e96448.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/892909e49156f7dcc0650fcd65243877.png)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
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2016-12-03更新
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4卷引用:2020届江苏省连云港市六所四星高中(海州高中、赣榆高中、海头中学、东海高中、新海高中、灌云高中)高三下学期模拟考试数学试题
2020届江苏省连云港市六所四星高中(海州高中、赣榆高中、海头中学、东海高中、新海高中、灌云高中)高三下学期模拟考试数学试题江苏省仪征中学2018—2019学年高二上学期期中考试数学试题(已下线)2013-2014学年浙江省嘉兴一中高二下学期期中理科数学卷(已下线)第三章 圆锥曲线与方程(选拔卷)-【单元测试】2021-2022学年高二数学尖子生选拔卷(苏教版2019选择性必修第一册)