名校
解题方法
1 . 已知椭圆
的离心率为
,且以原点为圆心,椭圆的焦距为直径的圆与直线
相切(
为常数).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/7f421cad-65e1-4b3b-b478-a4157982707d.png?resizew=211)
(1)求椭圆
的标准方程;
(2)如图,若椭圆的
左、右焦点分别为
,过
作直线
与椭圆分别交于两点
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b72ec972dde29dcf98a7ebd43ba3889.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/27/7f421cad-65e1-4b3b-b478-a4157982707d.png?resizew=211)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,若椭圆的
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c38928a92bc4b44ed3c9b89769f5372.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/e6670479a0083dd2dfd5ad55b47b1ab6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1cb67131cdb0d19fcd5c7b732e00a907.png)
您最近一年使用:0次
2017-11-28更新
|
1005次组卷
|
4卷引用:湖北省华中师范大学第一附属中学2018届高三上学期期中考试数学(文)试题
2 . 过点
的直线
与中心在原点,焦点在
轴上且离心率为
的椭圆
相交于
、
两点,直线
过线段
的中点,同时椭圆
上存在一点与右焦点关于直线
对称.
(1)求直线
的方程;
(2)求椭圆
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b094cba781181aeb90752170e9ba6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.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/2d585d2d6643471640905d234d9538c5.png)
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
您最近一年使用:0次
2017-11-21更新
|
603次组卷
|
2卷引用:湖北省部分重点中学2017-2018学年度上学期期中联考高二数学理科试题
名校
3 . 设离心率为
的椭圆
的左、右焦点为
, 点P是E上一点,
,
内切圆的半径为
.
(1)求E的方程;
(2)矩形ABCD的两顶点C、D在直线
上,A、B在椭圆E上,若矩形ABCD的周长为
, 求直线AB的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab0fe9059acc47d2447576e1260c4622.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f417db4a1faea572349497a820dc98cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2427943a38dcd93c9ec9b735ffc9fe5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a9df1061c3ba5151ba2f7359acaf356.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34e01955f8c8fe2f0041b35d8d602a7.png)
(1)求E的方程;
(2)矩形ABCD的两顶点C、D在直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c31c4f39399ec245a67db2933ed639f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1445c58e9918a2692f579ae73495a08.png)
您最近一年使用:0次
2017-10-14更新
|
1481次组卷
|
5卷引用:湖北省仙桃中学2018-2019学年高三上学期期中数学(理)试题
湖北省仙桃中学2018-2019学年高三上学期期中数学(理)试题江西师大附属中学2017届高三10月月考数学(理)试题江西师范大学附属中学2018届高三10月月考数学(理)试题(已下线)专题41椭圆-2022年(新高考)数学高频考点+重点题型(已下线)第3章 圆锥曲线与方程(章末测试提高卷)-2021-2022学年高二数学同步单元测试定心卷(苏教版2019选择性必修第一册)
解题方法
4 . 已知椭圆![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
的离心率为
,
,
,
,
的面积为
.
(1)求椭圆的标准方程;
(2)设直线
与椭圆
相交于
两点,是否存在这样的实数
,使得以
为直径的圆过原点,若存在,请求出
的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5bbb709522dba9425a6b45ee671298.png)
![](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/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3160fc73f2a90ae4a1a97351ab2673b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9199b50dd0036be9b764c621d1d46f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
(1)求椭圆的标准方程;
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acd55f837e9c4e6bba1163ef13edd09b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5ad58997b9dc0b341c9af08f0cd1fbe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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11-12高三上·北京朝阳·期末
5 . 如图,设椭圆
的左、右焦点分别为F1,F2,上顶点为A,过点A与AF2垂直的直线交x轴负半轴于点Q,且
0,若过 A,Q,F2三点的圆恰好与直线
相切,过定点 M(0,2)的直线
与椭圆C交于G,H两点(点G在点M,H之间).(Ⅰ)求椭圆C的方程;(Ⅱ)设直线
的斜率
,在x轴上是否存在点P(
,0),使得以PG,PH为邻边的平行四边形是菱形?如果存在,求出
的取值范围;如果不存在,请说明理由;(Ⅲ)若实数
满足
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/40dfbee4c2234064ddfc751af675c181.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcc89a6617c3c0da8e9961c331181a73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ecb427fb0ccc1c0565323b71ac97a36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ce619c464f2aa04178ea0111ba60544.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07550f93b4a2e3d7d83291f84afab494.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c62e7c58606b2250c6d189d85a6ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da1abd73732566f5c16bfb2b23b362be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c62e7c58606b2250c6d189d85a6ea8.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/2/7f35b91a-9172-4ea4-b880-5169c35678f8.png?resizew=209)
您最近一年使用:0次
2017-04-26更新
|
662次组卷
|
5卷引用:2016-2017学年湖北省七校(荆州中学、襄阳五中、襄阳四中等)高二下学期期中联考数学(理)试卷
名校
解题方法
6 . 已知椭圆
的中心在原点
,焦点在
轴上,离心率为
,右焦点到右顶点的距离为1.
(1)求椭圆
的标准方程;
(2)是否存在与椭圆
交于
两点的直线
,使得
成立?若存在,求出实数
的取值范围;若不存在,请说明理由.
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)是否存在与椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/817c1fe5a88bee1d94bbe552e20b718f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f14a642d824a7e4ec6f754526095ba6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95b3723770b29872c6a7a096d8b39efb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
您最近一年使用:0次
2017-02-26更新
|
727次组卷
|
6卷引用:湖北省宜昌市部分示范高中教学协作体2016-2017学年高二下学期期中考试数学(文)试题
解题方法
7 . 1.已知椭圆C:
的离心率为
,椭圆C的长轴长为4.
(1)求椭圆C的方程;
(2)已知直线
与椭圆C交于A,B两点,是否存在实数k使得以线段AB为直径的圆恰好经过坐标原点O?若存在,求出k的值;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C的方程;
(2)已知直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ff3ca9d16ea262007adb2d58467d78d.png)
您最近一年使用:0次
解题方法
8 . 已知椭圆的中心为原点,焦点在
轴上,离心率为
,且经过点
,直线
交椭圆于异于M的不同两点
.直线
轴分别交于点
.
(1)求椭圆标准方程;
(2)求
的取值范围;
(3)证明
是等腰三角形.
![](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/a3ba9d9535a1d7e34f66db9da0861394.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7d00a5df9d281dd4e1e45bf6a4d6fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/677a5973ae6d126f3660b776a007a1a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cf9b288c48c73463a2f214f02b6952a.png)
(1)求椭圆标准方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(3)证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eadb6f330e2d5325adb08c2b1d80b1ae.png)
您最近一年使用:0次
9 . 已知圆
,直线
,且直线
与圆
交于
两点.
(1)若
,求直线
的倾斜角;
(2)若点
满足
,求此时直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59c406915922045153a67d269f41ac4d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3445947fa34dd409a1354786e6c4a579.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed79cde317cee7f73037f66f52f02a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a54dbf1347334c75d15d7e53e078ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2016-12-03更新
|
676次组卷
|
3卷引用:2014-2015学年湖北省部分重点中学高二上学期期中考试理科数学试卷
14-15高二上·河北邢台·阶段练习
名校
10 . 已知中心在原点的椭圆
的左焦点
,右顶点
.
(1)求椭圆
的标准方程;
(2)斜率为
的直线
与椭圆
交于
两点,求弦长
的最大值及此时
的直线方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82cebd2b47374e5e73183a28b0e728cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84fa2706ef7722984553795c5afc0261.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)斜率为
![](https://img.xkw.com/dksih/QBM/2014/12/23/1571930690723840/1571930696073216/STEM/f3a3cd65f2334332a880b9e79da321f5.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/c7bdc75c9a9fba398e737d4832101f60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c413aa88023cf0b230c86a5530260a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2016-12-03更新
|
1916次组卷
|
5卷引用:湖北省黄石市有色第一中学2020-2021学年高二下学期期中数学试题
湖北省黄石市有色第一中学2020-2021学年高二下学期期中数学试题(已下线)2014-2015学年河北省邢台市二中高二上学期第二次月考理科数学试卷(已下线)2014-2015学年河北省邢台市二中高二上学期第二次月考文科数学试卷山西省朔州市怀仁一中2018-2019学年高二(上)第四次月考数学(理科)试题(b卷)(已下线)【南昌新东方】江西省南昌一中2020-2021学年高二上学期10月第一次月考数学(理)试题