1 . 已知椭圆
:
,
,
分别为椭圆
的左顶点和右焦点,过
的直线
交椭圆
于点
,
若
,且当直线
轴时,
.
的方程;
(2)设直线
,
的斜率分别为
,
,问
是否为定值?并证明你的结论;
(3)记
的面积为
,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48da128547c4cf9745e8e4b99988a3db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.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/a0ed1ec316bc54c37c4286c208f55667.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/e7b3447d466ec8f2fc3b4898720a82c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ae341f580ff8fbf21f616fe900b0e4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/165a501b2e6a3acc46212e59a166c053.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f1c40ebcc993a5778478154c124f0c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/20a541b81584a032f571159ea152c85a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84d454c82d9e52747563d47b68099249.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6defc43285a40f7ccb74c1cc04265eba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423b7ae39db552e60ee8b1d27312306f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4757181824e15e0f21e5bdd55448783.png)
(3)记
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9763846b1131e1e3e2d741ad95d5bb0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
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解题方法
2 . 已知椭圆
的右焦点是
,过点
的直线交椭圆
于
两点,若线段
中点
的坐标为
.
(1)求椭圆
的方程;
(2)已知
是椭圆
的下顶点,如果直线
交椭圆
于不同的两点
,且
都在以
为圆心的圆上,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/967dc76338e277e690e0e524d4179e1b.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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9efc447b298e9d697770c34298a2483c.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cbb6666f63b9f4832e573039a28ef6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cf8085c9d6fc73d634c7c316a14df78.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/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
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3 . 月光石不能频繁遇水,因为其主要成分是钾钠硅酸盐.一块斯里兰卡月光石的截面可近似看成由半圆和半椭圆组成,如图所示,在平面直角坐标系,半圆的圆心在坐标原点,半圆所在的圆过椭圆的右焦点
,半椭圆的短轴与半圆的直径重合.若直线
与半圆交于点
,与半椭圆交于点
,则
的面积是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/46f55a44-f8d2-4638-b34d-86b26d7dd0ba.png?resizew=170)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13282fb5922a6c61df3ac17cec9c9eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/46da94f346d9899ebc006231f1ee3fb6.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/004104bafb5f30338123d4ea2b7fedde.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/8/46f55a44-f8d2-4638-b34d-86b26d7dd0ba.png?resizew=170)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 已知A,B两点的距离为定值4,平面内一动点
,记
的内角A,B,C的对边分别为a,b,c,面积为
,下面说法正确的是(
)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02589faa1981626127e0463659e5880.png)
A.若![]() ![]() |
B.若![]() ![]() ![]() |
C.若![]() ![]() ![]() |
D.若![]() ![]() |
您最近一年使用:0次
2023-11-22更新
|
327次组卷
|
3卷引用:安徽省六安第一中学2023-2024学年高二上学期期中考试数学试题
安徽省六安第一中学2023-2024学年高二上学期期中考试数学试题四川省眉山市彭山区第一中学2023-2024学年高二上学期12月月考数学试题(已下线)河南省信阳市信阳高级中学2023-2024学年高二上学期1月测试数学试题
5 . 在平面直角坐标系
中,已知椭圆
的右焦点
坐标是
,且椭圆
上的点到
距离的最大值为
,过点
的直线交椭圆
于点
.
(1)求椭圆
的方程;
(2)设
为椭圆上一点,且满足
(
为坐标原点),当
时,求实数
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c38d8390234e0cb46172c8e2b02ea516.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b23a03ca8f1729bfcadf513784817fc5.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/ab46ea0cba2d06283fae3d864a2329e0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a7908e8e2ca67ad0f739860222423950.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd6c84e127366a8840b6720a9dacd8bd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4f263df3ae9b354401c14685be256f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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解题方法
6 . 已知椭圆
的左、右焦点分别为
,
,O为坐标原点,点
在椭圆C上,且
,直线
过点
且与椭圆C交于A,B两点.
(1)求椭圆C的标准方程;
(2)已知
,
,若直线
,
交于点D,探究:点D是否在某定直线上?若是,求出该直线的方程;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.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/a216c108cb54c2b3845ac7dce1ed10a0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e02c3677ab351b6195ae325b971a8573.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
(1)求椭圆C的标准方程;
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3afced09f15e80420611e9199c41fb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/024494ac1df3b60ddcaa0cef4940ca87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7785afeeaf274892253d04b4f693b367.png)
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解题方法
7 . 已知椭圆
的左、右焦点分别为
,该椭圆的离心率为
,且椭圆上动点
与点
的最大距离为3.
(1)求椭圆
的方程;
(2)如图,若直线
与
轴、椭圆
顺次交于
(点
在椭圆左顶点的左侧),且
,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad523e69a1bf925e73a22900b9855df2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d2a97987f71835f519b462f5b8f5957.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/12/12/90384f10-0981-4eb0-8516-f9041f385bac.png?resizew=238)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)如图,若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](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/89fc107c4b33d6dd648b396156494ea9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0e389667b3385eee57f681b500a04a2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d0b4efdd1bb37691c5473e53a748e44c.png)
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2023-11-17更新
|
546次组卷
|
4卷引用:安徽省A10联盟2023-2024学年高二上学期11月期中考试数学试题
名校
解题方法
8 . 一动圆与圆
外切,同时与圆
内切,动圆圆心的轨迹为曲线
.
(1)求曲线
的方程;
(2)点
为
上一动点,点
为坐标原点,曲线
的右焦点为
,求
的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d008f0825083c74d3da4d87db1eab440.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/869b84b96637d80f7dbb2bde218a4e72.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/121fdb78e9812aa208a5efb708521011.png)
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2023-11-17更新
|
830次组卷
|
4卷引用:安徽省A10联盟2023-2024学年高二上学期11月期中考试数学试题
解题方法
9 . 已知曲线
为椭圆,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a162350ece716cb466f0476aed341a76.png)
A.![]() |
B.若![]() ![]() ![]() ![]() |
C.若![]() ![]() ![]() ![]() |
D.若![]() ![]() ![]() ![]() |
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10 . 已知椭圆
经过
两点.
(1)求
的方程;
(2)设
为
的上顶点,过点
且斜率为
的直线与
相交于
两点,且点
在点
的下方,点
在线段
上,若
,证明:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f04443a0c1cf4808aea741c9f9379b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f11f00b003a6ffc40ffe5cb215e7e364.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a4d8e0f539ec84b3b97dc230522018f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad056c25c0fdcbcc765eb5cbc6093f2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/49b50357a6545cae8348e3059312f520.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07e02e4d1b5550806ff570644d8c0aa9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/34c44545f96b900371d43309252281c1.png)
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