名校
解题方法
1 . 已知椭圆
过点
,离心率为
,点
分别为其左右焦点.
(1)求椭圆
的标准方程;
(2)若
上存在两个点
,椭圆上有两个点
满足
三点共线,
三点共线,且
,求四边形
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84e2f2d391b1e6304eb2bba560d0ccdd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdd670bd3726ea58ab5c46c245d05559.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/745de5ef1fd897d16e37464172d5e8c9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d3d676ff4bf2f8e136835a0a702ebe53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c485045b8cc718cfabee23fe984f82a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86859f48d33b5163960bef221b189b7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99393efa04579f3db5cf4f7e319f0440.png)
您最近一年使用:0次
2016-12-03更新
|
1437次组卷
|
6卷引用:2016届河北省正定中学高三上学期期中数学试卷
2 . 已知椭圆
上一点M的纵坐标为2.
(1)求M的横坐标;
(2)求过点M且与
共焦点的椭圆方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/66ae68807a1faa5752f55ce5bd643f83.png)
(1)求M的横坐标;
(2)求过点M且与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81bdc07367292653484aa6e5a121b757.png)
您最近一年使用:0次
2016-12-03更新
|
685次组卷
|
3卷引用:2015-2016学年河北邯郸曲周县一中高二上学期第二次月考理科数学卷
解题方法
3 . 已知椭圆
经过点
,离心率为
.
(1)求椭圆
的方程;
(2)不垂直与坐标轴的直线
与椭圆
交于
两点,线段
的垂直平分线交y轴于点
,若
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e684712aade8dcebb62716843791034.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)不垂直与坐标轴的直线
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eff26171e5cdbb425f8c7642f3a1ec7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe17db75cdacde06262271d174307d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
14-15高三上·河北衡水·阶段练习
解题方法
4 . 已知椭圆
的左、右焦点分别为
,椭圆的离心率为
,且椭圆
经过点
.
(1)求椭圆
的标准方程;
(2)若线段
是椭圆过点
的弦,且
,求
内切圆面积最大时实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0dfb290b1a84f670549554a0c988593.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/697b2c535494b5acb51388f5c8428879.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36f744ab198210340a54adb2ae4a6b9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
12-13高三·天津·阶段练习
解题方法
5 . 已知椭圆
的一个焦点为
且过点
.
![](https://img.xkw.com/dksih/QBM/2018/8/22/2015983746736128/2016726972760064/STEM/35a34bb8ba694bc68badacce0e4c9699.png?resizew=222)
(Ⅰ)求椭圆
的方程;
(Ⅱ)设椭圆
的上下顶点分别为
是椭圆上异于
的任一点,直线
分别交
轴于点
,若直线
与过点
的圆
相切,切点为
.
证明:线段
的长为定值,并求出该定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a200ca2c4af794f4d1c6a5443830b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17618d8d22ebb3fd6835a7eb139b4f95.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27208f7c8d1f32587bcb0a52dbc40c56.png)
![](https://img.xkw.com/dksih/QBM/2018/8/22/2015983746736128/2016726972760064/STEM/35a34bb8ba694bc68badacce0e4c9699.png?resizew=222)
(Ⅰ)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(Ⅱ)设椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15bebf4417f17ba00e6e1f98ff4c5717.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/941580b384bf5aa122b56dec5f0e5cb7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be452c8bdea6b4e4c7a6d96e9dc6a51c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b68df477b3ee45ac0f725db00d465a1.png)
证明:线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be99fa94a1f3e4964fcc13a14fab9ba5.png)
您最近一年使用:0次
2016-12-02更新
|
1250次组卷
|
3卷引用:河北省衡水中学2020届高三高考数学(文科)一模试题
9-10高二下·河南郑州·期末
解题方法
6 . 设
分别为椭圆
的左、右两个焦点.
(1)若椭圆
上的点
到
两点的距离之和等于4,求椭圆
的方程和焦点坐标;
(2)设点P是(1)中所得椭圆上的动点,
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
(1)若椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/315a24a74c99dfa18e6d8b1b5220724b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点P是(1)中所得椭圆上的动点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49f274a6fb62ddc16a07565d54006985.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
您最近一年使用:0次
2016-12-03更新
|
578次组卷
|
5卷引用:2015-2016学年河北省望都中学高二10月月考文科数学试卷
2015-2016学年河北省望都中学高二10月月考文科数学试卷(已下线)郑州智林学校09-10学年高二下学期期末考试数学试卷(理科)(已下线)2011-2012年福建省福州市八中高二上学期期末考试理科数学2014-2015学年甘肃省兰州一中高二上学期期末考试数学试卷2016-2017学年山东桓台二中高二9月月考数学试卷
2012·河北·一模
解题方法
7 . 已知方向向量为
的直线l过椭圆
的焦点以及点
,直线l与椭圆C交于 A 、B两点,且A、B两点与另一焦点围成的三角形周长为
.
(1)求椭圆C的方程.
(2)过左焦点
且不与x轴垂直的直线m交椭圆于M、N两点,
(O坐标原点),求直线m的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c6e29f20f663e2b227557e22546dd98.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b25c39d90e723c654b028d4286d05d73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ee05b3210c8964deef8ff771173d288.png)
(1)求椭圆C的方程.
(2)过左焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4f325af38df329028f8791eb13e386.png)
您最近一年使用:0次
2012·河北唐山·一模
解题方法
8 . 中心在原点O,焦点
在x轴上的椭圆E经过点C(2, 2),且![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d51ae46ce7f78185af92c923c1ac35.png)
(1)求椭圆E的方程;
(2)垂直于OC的直线l与椭圆E交于A、B两点,当以AB为直径的圆P与y轴相切时,求直线l的方程和圆P的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/979153fd6f13481ca1dbd53dc9349518.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42d51ae46ce7f78185af92c923c1ac35.png)
(1)求椭圆E的方程;
(2)垂直于OC的直线l与椭圆E交于A、B两点,当以AB为直径的圆P与y轴相切时,求直线l的方程和圆P的方程.
您最近一年使用:0次
11-12高二下·河北衡水·阶段练习
9 . 已知抛物线
的焦点
以及椭圆
的上、下焦点及左、右顶点均在圆
上.
(1)求抛物线
和椭圆
的标准方程;
(2)过点
的直线交抛物线
于
、
两不同点,交
轴于点
,已知
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c518a09919976d184de6ee1c5dec4b48.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/83de9a16fe69aa19744801693652be7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/560adea7b0d4fbe4131fc41f3fcbd871.png)
(1)求抛物线
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/93f38efbc14041c2be89dc0577ab8df8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/e966c9fed75c4e6181a62c4a5cc261d9.png)
(2)过点
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/769ad5ed395a48ca932943309bed59dc.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/93f38efbc14041c2be89dc0577ab8df8.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/acf674bda8a3497bb8c2cf93bd59f47e.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/55bd1e65687c4ff9b4d387dbcdebfdec.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/3491c81e10734d34b9b8c3e86933f59b.png)
![](https://img.xkw.com/dksih/QBM/2015/6/19/1572135933853696/1572135940071424/STEM/fd413e6d44a24a3ba27eda3145770c79.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8887db8acd21bcb971ccf7f56ef1935f.png)
您最近一年使用:0次
2012·河北石家庄·一模
解题方法
10 . 已知焦点在
轴上的椭圆C1:
=1经过A(1,0)点,且离心率为
.
(1)求椭圆C1的方程;
(2)过抛物线C2:
(h∈R)上P点的切线与椭圆C1交于两点M、N,记线段MN与PA的中点分别为G、H,当GH与
轴平行时,求h的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e84aa1cf44d13200c785111c2b410a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆C1的方程;
(2)过抛物线C2:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e31401ce101641b9022a4c6a191d88d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
您最近一年使用:0次