2024高二上·全国·专题练习
解题方法
1 . 分别写出满足下列条件的椭圆的标准方程:
(1)焦距为4,且经过点
;
(2)求经过点
和点
的椭圆方程.
(1)焦距为4,且经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dba0ddcdf6ed46447b5d4885674700a9.png)
(2)求经过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bddd5d20576fb15ced9e028d965e708.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ac101eab8342edcef93ae13226dbf45.png)
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解题方法
2 . 已知椭圆
的离心率
在椭圆上.
(1)求椭圆
的标准方程;
(2)已知动直线
(斜率存在)与椭圆相交于点
两点,且
的面积
,若
为线段
的中点.
点在
轴上投影为
,问:在
轴上是否存在两个定点
,使得
为定值,若存在求出
的坐标;若不存在,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01bd04850467c1df65541e93912c167f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1f0417d8269f01d8e0bc1a8756e2ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1731169574e86f63684590a8b8f67df3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4ccd4537f4dee2050ade38b972eb9b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b397875f3272bf8bc0cc50c2cda53ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00442d96d695db2c58bf1fb7165fca94.png)
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解题方法
3 . 已知椭圆
的上顶点为
,右顶点为
,且直线
的斜率为
.
(1)求
的方程;
(2)若直线
与
交于
两点(异于点
),且满足
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/383f12cb70ca55eba4ff012771dbfa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3389f53711264b0acba3ba6019f8b908.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8573fd86670b02e982d52330b24d7d93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7a551505ae42b49904bab59b17012d8.png)
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2024-01-31更新
|
235次组卷
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5卷引用:2.2.1 椭圆的标准方程(十三大题型)(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)
(已下线)2.2.1 椭圆的标准方程(十三大题型)(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)河南省部分名校2023-2024学年高二上学期1月期末考试数学试题河南省焦作市2023-2024学年高二上学期1月期末考试数学试题河南省周口市沈丘县第三高级中学2023-2024学年高二上学期期末数学试题河南省濮阳市2023-2024学年高二上学期期末考试数学试题
2024高二·全国·专题练习
解题方法
4 . 已知椭圆C:
左、右焦点分别
、
,长轴长为
,且椭圆C的离心率与双曲线
的离心率乘积为1,P为椭圆C上一点,直线
交椭圆C于另一点Q.
(1)求椭圆C的方程;
(2)若
且
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/347b68f42934c74e0d759a67613a1da9.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/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5848e50805496263d52dcbde9671a89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ac86e1c253297a377e14fb9a1689be8.png)
(1)求椭圆C的方程;
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b3a13734195a719ce99f922fc851517.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a69902eeb2fe982065f7ba6cd42ea60b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a5215b714cde3ed7790b3ed4f6711c3.png)
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5 . 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: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)
(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)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
解题方法
6 . 已知椭圆
,离心率为
,短轴长为
.
(1)求椭圆
的方程;
(2)过坐标原点
且不与坐标轴重合的直线
交椭圆
于
,
两点,过点
作
轴的垂线,垂足为
,直线
与椭圆的另一个交点为
.求证:
为直角三角形.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/026fced6e02fab3a836d0f0280d3f3bf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过坐标原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf3d566704b44ea4ef1f99c37bd46902.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a9dabb53dc826019fc8b6ae6d940c5.png)
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解题方法
7 . 已知点
为椭圆
的左焦点,
在C上.
(1)求C的方程;
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
,
,且
.
①当
时,求四边形
的面积;
②求四边形
的面积最大时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e1a85a657231ef717809d5a839ad9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f2f483905437b31b8f60e2d388ec806.png)
(1)求C的方程;
(2)记(1)中轨迹为曲线C,在曲线C的上半部分取两点M,N,若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53e4a3aea4b4b0d87c014030a6ff9027.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/451fc6e4248b63e70595f23842f06c93.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe98ef73331666776210e74ea36555f8.png)
①当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5b032d78f28236864b69803022e442b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
②求四边形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a75bfa01c4013b4710a7fb71c305c0b7.png)
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2024-01-22更新
|
569次组卷
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3卷引用: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)
(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)福建省厦门市厦门外国语学校2023-2024学年高二上学期期末模拟考试数学试题江西省南昌市第二中学2024届高三“九省联考”考后适应性测试数学试题(二)
8 . 已知椭圆
:
(
)过点
,过其右焦点
且垂直于
轴的直线交椭圆于
,
两点,且
.
(1)求椭圆
的方程;
(2)若矩形
各边均与椭圆
相切,
①证明:矩形
的对角线长为定值;
②求矩形
周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7aea48c44781a844b5c19191f70f61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a2e200b0886d91a1f9d536b897f2361.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/236f52e04ddbd7253f44b97c4756ef9c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
①证明:矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
②求矩形
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/389bc3f29c058067e06e0d0d2be399da.png)
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9 . 已知椭圆的焦点坐标为
,短轴长为4,则椭圆的标准方程为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a80fd8b6f1f56304198b3fe89accd3f.png)
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2024-01-20更新
|
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4卷引用:2.2.1 椭圆的标准方程(十三大题型)(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)
(已下线)2.2.1 椭圆的标准方程(十三大题型)(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)上海市莘庄中学2023-2024学年高二上学期期末数学试题 上海市杨浦高级中学2023-2024学年高二下学期3月月考数学试卷(已下线)专题04 圆锥曲线(六大题型+优选提升题)-【好题汇编】备战2023-2024学年高二数学下学期期末真题分类汇编(沪教版2020选择性必修,上海专用)
名校
解题方法
10 . 若焦点在
轴上的椭圆
的焦距为
,则实数
的值为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/526f7557e886d71cc74ace5078b56431.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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2023-12-06更新
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4卷引用:2.2.1 椭圆的标准方程(十三大题型)(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)
(已下线)2.2.1 椭圆的标准方程(十三大题型)(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)江苏省高邮市2023-2024学年高二上学期12月学情调研测试数学试卷新疆维吾尔自治区石河子市第一中学2023-2024学年高二上学期12月月考数学试题上海市上海外国语大学附属外国语学校松江云间中学、进才中学、交大附中嘉定分校、复旦附中青浦分校2023-2024学年高二上学期四校联考数学试卷