1 . 椭圆
的离心率
,且椭圆
的长轴长为4.
(1)求椭圆
的方程;
(2)设直线
过点
,且与椭圆
相交于
两点,又点
是椭圆
的下顶点,当
面积最大时,求直线
的方程,并求出最大面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5de85df85401e7e8da683ea4a784963c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b261ae2fe9a7cba043c88af2d4be3cc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2024-01-23更新
|
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3卷引用:湖北省恩施州利川市第一中学2023-2024学年高二下学期开学考试数学试题
湖北省恩施州利川市第一中学2023-2024学年高二下学期开学考试数学试题宁夏回族自治区银川市贺兰县第一中学2023-2024学年高二上学期期末数学试题(已下线)2.2.2 椭圆的性质(十八大题型)(分层练习)-2023-2024学年高二数学同步精品课堂(沪教版2020选择性必修第一册)
2 . 已知椭圆
(常数
),点
,
,
为坐标原点.
(1)求椭圆离心率的取值范围;
(2)若
是椭圆
上任意一点,
,求
的取值范围;
(3)设
,
是椭圆
上的两个动点,满足
,试探究
的面积是否为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3044df061f3c9b06e525722cca969a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/655b06387179d53c1e474fcfcb408b1e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2801ced7e4279a7c4a98749d3d3118b1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14fec153773d15346d7cf3fc34d290f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
(1)求椭圆离心率的取值范围;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/385495ec3ecd33e95b9b671ccc2866b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8198c3b302b3820e86763428eb1e91cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3463ced6030af957f13f9ba05b977c1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f435efcc7869eec21bdba1ed81dc3f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/392d00243d81bf17ff3be81e7a7ee05c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25dd698d57d1cf239eb8752aecaaa4f4.png)
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2023-11-21更新
|
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4卷引用:湖北省恩施州利川市第一中学2023-2024学年高二下学期开学考试数学试题
名校
3 . 已知椭圆
的焦距为2,过椭圆
的右焦点
且不与两坐标轴平行的直线交椭圆
于
,
两点,若
轴上的点
满足
且
恒成立,则椭圆
离心率
的取值范围为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f30acc34f4ee1077532ae6808af2ab2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e3aecfed6162d24874f81e9b577e01f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
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2023-01-18更新
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5卷引用:湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期末数学试题
名校
解题方法
4 . 已知椭圆
的离心率为
,
,
分别为椭圆的左、右焦点,P为椭圆的下顶点,且
的面积为4.
(1)求椭圆C的方程:
(2)圆
,点A,B分别是椭圆C和圆
上位于y轴右侧的动点,且直线PB的斜率是直线PA的斜率的2倍,求证:直线AB恒过定点
![](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/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/002ed1ebb2cb936e10ab478789f91c7c.png)
(1)求椭圆C的方程:
(2)圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73e25b317906ca42ab1c73779cb462ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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2022-12-06更新
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5卷引用:湖北省恩施州巴东县第一高级中学2023-2024学年高二上学期末数学试题