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1 . 已知椭圆C:
(a>b>0)的左右焦点分别为F1(-c,0)和F2(c,0),上顶点为M,且△MF1F2为等边三角形,点M到左右顶点的距离之和为
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/a2fcba21-0725-470a-8c9a-3c116b953510.png?resizew=270)
(1)求椭圆C的标准方程;
(2)过点F1的直线l交椭圆C于A,B两点,若以AB为直径的圆经过点F2,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dbff61fe9d4e93d7cc338489d1c99c40.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/9/a2fcba21-0725-470a-8c9a-3c116b953510.png?resizew=270)
(1)求椭圆C的标准方程;
(2)过点F1的直线l交椭圆C于A,B两点,若以AB为直径的圆经过点F2,求直线l的方程.
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2 . 点P在椭圆
上,
为左焦点,且线段
的中点M在y轴正半轴上,则以线段
为直径的圆的标准方程为_________ ,该圆上的动点A与椭圆上的动点B之间的最大距离为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ddab7b8aa22e1ba4c59da7dc04ac9e2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
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解题方法
3 . 已知椭圆
的左、右焦点为
,
,P是椭圆上的点,当点P在椭圆上运动时,
面积的最大值为4,当
轴时,
面积为
.
![](https://img.xkw.com/dksih/QBM/2020/11/27/2602194757746688/2606110916067328/STEM/17bd12fd9a07479c8871dc5c1ebfc0d0.png?resizew=299)
(1)求椭圆C的标准方程;
(2)如图,若直线
、
交椭圆另一点分别是A、B,点P不在x轴上,且
,求点P的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6b0dadb875cccce870b69409a476606.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/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0aa9a6be97b5f275d55697fd3cd0a442.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33d776753746914c2410a3946c357f35.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://img.xkw.com/dksih/QBM/2020/11/27/2602194757746688/2606110916067328/STEM/17bd12fd9a07479c8871dc5c1ebfc0d0.png?resizew=299)
(1)求椭圆C的标准方程;
(2)如图,若直线
![](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/c50c55951be894ce25e131c7cc19e45d.png)
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4 . 已知斜率为
的直线l与椭圆
交于A,B两点,线段AB中点M纵坐标为
,点
在椭圆上,若
的平分线交线段AB于点N,则
的值MN为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74f7981bd8103fb549c776401005fb12.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68b572cbfe5491fabd42a5fdd4038a50.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4035e86d5a20db38e0f349e20423f0d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb686e4f5e3938575bc547e849d5513f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a03352aca9b5d795c78dc7f143edc2c2.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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5 . 已知椭圆E的中心在坐标原点,两个焦点分别为
,
,短半轴长为2.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/9fd3418d-c32e-4d3b-a469-48b0921fbbe9.png?resizew=173)
(1)求椭圆E的标准方程;
(2)过焦点
的直线l交椭圆E于A,B两点,满足
,求直线l的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9d55173f26afdf0e37462b556a605.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b6d6f746c2355072d914591bf60c3801.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/9fd3418d-c32e-4d3b-a469-48b0921fbbe9.png?resizew=173)
(1)求椭圆E的标准方程;
(2)过焦点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49d0c7e52cee8894b483ccf22c836845.png)
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2019-12-23更新
|
388次组卷
|
2卷引用:重庆市云阳县2019-2020学年高二上学期期中考试数学(文)试题
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6 . 已知椭圆
的左右焦点分别为
,且
为抛物线
的焦点,
的准线被
和圆
截得的弦长分别为
.
(1)求
方程;
(2)已知动直线
与抛物线
相切(切点异于原点),且与椭圆
相交于
两点,若椭圆
上存在点
,使得
,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79c9c87eba774f6bc072663d32d11fc4.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/1e4be819fc47b2aa19ab2022b3dfeb6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/202aef7d560bb52f493e11159cc6cc41.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
(2)已知动直线
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daa85ab7da6e54aaea66a5b3b1ef6e8b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
您最近一年使用:0次
2018-11-30更新
|
897次组卷
|
5卷引用:【全国百强校】重庆市第一中学2019届高三上学期期中考试数学(理)试题