已知椭圆
:
的左、右顶点分别为
,
,离心率为
,点
在椭圆
上.
(1)求椭圆
的方程.
(2)若过点
且斜率不为0的直线与椭圆
交于
,
两点,已知直线
与
相交于点
,试判断点
是否在定直线上?若是,请求出定直线的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad7451b947d1adea22bc04070efdd2b0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9721059d158853671eaf19e39769b13.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8db4b168ddbcba90ac9b31d36a0432.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da40c0caa13092a358d73cdbd65c4c78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/63314cb1e0f1891396c8dbaa4339444c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
(2)若过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03892233334847c77808af05e9a7abe8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00a28be4d5a16cf245f6fa7c4088fee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9eeee83b4b7c6ceac7828ff534ce15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3870b1df343c9806470ca8733dd4eb89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/628acd3776874807ab2b8c55467311f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc3e8a1475b983d1a4295db0e16d4c2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afc3e8a1475b983d1a4295db0e16d4c2.png)
21-22高二上·福建泉州·期中 查看更多[2]
更新时间:2022-10-26 08:38:02
|
相似题推荐
【推荐1】已知椭圆
的左、右焦点分别是
,其离心率
,过
且垂直于
轴的直线被椭圆
截得的线段长为1.
(1)求椭圆
的方程;
(2)点
是椭圆
上除长轴端点外的任一点,过点
作斜率为
的直线
,使得
与椭圆
有且只有一个公共点,设直线
的斜率分别为
,若
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为定值,并求出这个定值;
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上除长轴端点外的任一点,设
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的长轴于点
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42623f14667ebfa914eb12d026023d6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
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(3)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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解题方法
【推荐2】已知点F是椭圆C:
的右焦点,过点F的直线l交椭圆于M,N两点.当直线l过C的下顶点时,l的斜率为
;当直线l垂直于C的长轴时,
的面积为
.
(1)求椭圆C的标准方程;
(2)当
时,求直线l的方程;
(3)若直线l上存在点P满足
,且点P在椭圆外,证明:点P在定直线上,并求出该直线的方程.
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(1)求椭圆C的标准方程;
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【推荐1】已知椭圆C:
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(1)求椭圆C的标准方程;
(2)过点F的直线l与椭圆C交于M,N两点,过点M作直线x=3的垂线,垂足为点P,证明直线NP经过定点,并求出这个定点的坐标.
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4d9ff190d74979422dae71751c6fba.png)
(1)求椭圆C的标准方程;
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【推荐2】已知椭圆
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交于不同的两点
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.
(1)求椭圆
的方程;
(2)若已知点
,求
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(1)求椭圆
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(2)若已知点
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解答题-证明题
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适中
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【推荐1】已知椭圆
:
,若点
,
,
,
中恰有三点在椭圆
上.
(1)求
的方程;
(2)点
是
的左焦点,过点
且与
轴不重合的直线
与
交于不同的两点
,
,求证:
内切圆的圆心在定直线上.
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7b67c0525a41fffd3ff86fded5ce46c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa147625926cc1453cc20b42f0685a69.png)
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(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)点
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ad3a4d8eb0a4f3dd417124a19f60066.png)
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【推荐2】已知椭圆
的离心率为
,短轴的下端点
的坐标为
.
(1)求椭圆
的方程;
(2)设
,
是椭圆
上异于
且不关于
轴对称的两点,
,
的中点为
,求证:点
在定直线上运动.
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)设
![](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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
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![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
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