名校
解题方法
1 . 阿基米德不仅是著名的物理学家,也是著名的数学家,他利用“逼近法”得到椭圆的面积除以圆周率等于椭圆的长半轴长与短半轴长的乘积.若焦点在
轴上的椭圆
的离心率为
,面积为
,则椭圆
的标准方程为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b2a698891d42c70b597f0da4f215f09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bf850c14f7a7679efe616c306afecbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2024-01-13更新
|
324次组卷
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2卷引用:云南省保山市腾冲市民族中学2023-2024学年高二下学期开学摸底考试数学试卷(A卷)
名校
解题方法
2 . 已知椭圆E:
离心率为
,且经过点
.
(1)求椭圆E的方程;
(2)过点
且斜率不为0的直线
与椭圆C交于M,N两点,证明:直线
与直线
的斜率之积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
(1)求椭圆E的方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9da30f3b77f2318f2000fa009979f04c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
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|
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2卷引用:云南省开远市第一中学校2023-2024学年高二下学期开学考试数学试题
3 . 已知椭圆
的两个顶点分别为
,焦点在
轴上,离心率为
.
(1)求椭圆
的方程;
(2)设
为原点,过点
的直线
交椭圆
于点
,直线
与直线
相交于点
,直线
与
轴相交于点
.求证:
与
的面积之比为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37e9c11cc36320090d0aaf0c621a63b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60f2a72c6d7780757ab065fb29f47526.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f50b3ae183997b707d16eb4e7f6712fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dda3804b1fa07570002ac27483947fc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed207009a48b69f1e76ba9a0d20f193a.png)
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2024-01-04更新
|
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4卷引用:云南省昆明市第三中学2023-2024学年高二下学期第一次综合测试数学试卷
4 . 如图,已知椭圆
的右焦点
与抛物线
的焦点重合,椭圆
的离心率为
,
是
与
的一个公共点,且
.
(1)求椭圆
与抛物线
的方程;
(2)直线
与椭圆
交于
两点(A在第一象限),直线
交椭圆
于另一点
,直线
交抛物线
于
两点,且使得
依次排序,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/727f39a1f3f3c48a5ed2e30693ddcbca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/544fc1ddf9f59d08c9feb5df9b4080d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bf31876698721a199c7c53c6b320aa86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/016d0f475f43324cbe76ac8468c14e0f.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/29/ad3034a4-2f4e-4b59-bfad-707bb5ad8269.png?resizew=150)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df5a0e5b12b88a5ab25b639c9afab445.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f80d0647ff3fc4a17b44719fb44691d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99d5e1e4b98c58a5f4ec33af0ed2acbc.png)
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|
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名校
解题方法
5 . 已知椭圆
的离心率为
,且过点
.
(1)求椭圆C的方程;
(2)若椭圆C的上顶点为P,过P的两条直线
,
分别与C交于异于点P的A,B两点,若直线
,
的斜率之和为
,试判断直线
是否过定点?若是,求出该定点;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/827ccf0c04aa941ba20d5f4c6068b46b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea2fc66af1e6967e988c9670ca8ceeee.png)
(1)求椭圆C的方程;
(2)若椭圆C的上顶点为P,过P的两条直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
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2023-11-09更新
|
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4卷引用:云南省昭通市水富市第一中学等三校联考2023-2024学年高二下学期开学考试数学试卷
解题方法
6 . 在平面直角坐标系
中,已知椭圆
的离心率为
,且过点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/9b6f38f4-2ba1-4be3-a568-c0c93f9c5340.png?resizew=222)
(1)求椭圆C的方程;
(2)如图所示,动直线
交椭圆C于A,B两点,交y轴于点M.点N是M关于O的对称点,
的半径为
.设D为
的中点,
与
分别相切于点E,F,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](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/182c81fb1c5e6d1a57a5f34a31ee69a9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/9/9b6f38f4-2ba1-4be3-a568-c0c93f9c5340.png?resizew=222)
(1)求椭圆C的方程;
(2)如图所示,动直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/327a8132cb929667c033a3c20bd9c67c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c22f4b5c09a56bd63d8378365fbdbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de246abb87d25da6150e81d4ce1d0a7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c818110255bdad691f61be6461a6fd73.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c22f4b5c09a56bd63d8378365fbdbf3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c962fe4f47732b8e6e83d17ff2b9af13.png)
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名校
解题方法
7 . 已知椭圆
的离心率为
,椭圆的长轴长为
.
(1)求椭圆C的方程;
(2)若直线
与椭圆C相交于A、B两点,点
,求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1174142f3bba761585b6bc2653009b36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b91d650c2fc1a741fabdb333b09aeb6.png)
(1)求椭圆C的方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae077b198c3e6a891ca7c5eb6d53482a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fc066778e4ffb4ba7645f51d0af535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7787dfab61ed9830b531da365e592bbd.png)
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|
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3卷引用:云南省大理白族自治州民族中学2023-2024学年高二下学期见面考试数学试题
名校
解题方法
8 . 已知椭圆
的离心率为
,过点
的直线与椭圆
交于
,
两点,且满足
.动点
满足
,则下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfba523ccc96ebcfcabc1d31ab59075d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a2a3989976ab78d8d6fb664ad672c9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3c9708ef0dc6d6f5dcf6596d3e4f6e5.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/ba4d488d56b95a44a6b0b40d3e89c010.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d73e034620351fd71c3d00adb1f447ac.png)
A.![]() |
B.动点![]() ![]() |
C.线段![]() ![]() ![]() |
D.线段![]() ![]() ![]() |
您最近一年使用:0次
2022-11-08更新
|
466次组卷
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7卷引用:云南省昆明市第五中学2023届高三上学期省测模拟数学试题(B卷)
云南省昆明市第五中学2023届高三上学期省测模拟数学试题(B卷)湖南省长沙市第一中学2023届高三上学期入学摸底考试数学试题江苏省南京市第一中学2023届高三上学期入学考试数学试题(已下线)专题37 求曲线的轨迹方程-2重庆市求精中学校2022-2023学年高二上学期期中数学试题浙江省金华十校2022-2023学年高二上学期期末联考模拟数学试题2(已下线)第五篇 向量与几何 专题5 调和点列 微点4 调和点列综合训练
解题方法
9 . 椭圆
的一个顶点为
,离心率
.
(1)求椭圆方程;
(2)若直线
与椭圆交于不同的两点
,
,且满足
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7dd54b9df3402ad91e2d34c40efe0c7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1394a4ed26d099cb02fb97ccb635f0f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/700f1ef8d7b90141e0150d6440427a43.png)
(1)求椭圆方程;
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4c311b215f3c3144fbe11ffacf386b3a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b485b62d004d52fb31d6ed99ccb7669.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2卷引用:云南省曲靖市罗平县第一中学2021-2022学年高二下学期见面考数学试题
名校
解题方法
10 . 已知椭圆
过点
,离心率为
,直线
与椭圆
交于
两点,过点
作
,垂足为C点,直线AC与椭圆
的另一个交点为
.
(1)求椭圆
的方程;
(2)试问
是否为定值?若为定值,求出定值;若不为定值,说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7e5578ca83f5bd5c285994061b9c015.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b8f9648c81481bb487a43f95c04d991.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d5989c84e320b504511f23eeb6e7357.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b343d77ee4dced82ecc479206c42977d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/69b5c1cad14908e18fd7bc8a96ca9580.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b45db8dd8768994af51206565379fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)试问
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/246a86f34603eaf2e6a948681b831b0d.png)
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2022-08-12更新
|
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4卷引用:云南省下关第一中学2023届高三上学期见面考数学试题