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1 . 已知曲线C:
(m,
),则下列说法正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2085af2326d0e13a12d3db8dbb79f51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb2bfd46447bdc5f025323d3cf5c008c.png)
A.若![]() ![]() ![]() |
B.若![]() |
C.若![]() |
D.曲线C可以是抛物线 |
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解题方法
2 . 把半椭圆:
和圆弧:
合成的曲线称为“曲圆”,其中点
是半椭圆的右焦点,
分别是“曲圆”与
轴的上、下交点,已知
,则半椭圆方程为_________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22178ee98809feea0b6d87241c7ba288.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7cdb94fa47eca1bbc1de89a3e45f3030.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/092fd1b1d33979818300cd2e3699bff7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04d468be20b4d43f5de75416de20e8ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c7b7f14b1c45551f812d9c301a4ffe60.png)
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3 . 已知椭圆
,在下列结论正确的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f3a8d8e6af4a0e845700317933d895c.png)
A.长轴长为1 | B.焦距为![]() |
C.焦点坐标为![]() | D.离心率为![]() |
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4卷引用:浙江省宁波市镇海中学2021-2022学年高二上学期期中数学试题
解题方法
4 . 求满足下列条件的椭圆标准方程:
(1)焦点坐标为
,并且椭圆上一点
到两焦点距离之和为10;
(2)经过两点
.
(1)焦点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e7debf142ea7f2b4039daeeae25a348.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
(2)经过两点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2f6f78e66c8ce4c87da553d667fd8714.png)
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5 . 已知
是平面上的动点, 且点
与
的距离之和为
.点
的轨迹为曲线
.
(1)求动点
的轨迹
的方程;
(2)不与
轴垂直的直线
过点
且交曲线
于
两点, 曲线
与
轴的交点为
,当
时,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3780c439ea559ac839f98bad07c9d9c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求动点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)不与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7789a500686c7a73770404ead6af0590.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/224d119270dcda6f3b9b88396ccb6d39.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2538654836f77efd416dd566198f55d4.png)
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6 . 已知曲线
上任意一点到点
的距离与到直线
距离之比为
,在曲线
上取
两点,使得线段
的中点
在圆
上.
(1)求曲线
的方程:
(2)若
为坐标原点,求
面积的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8e117f70e24d9d5fb2ed7f43eb87d7d6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da311e04b37bfd1738a879db46a90d7d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d61985901c2bc698d72ac88f4e1eb65.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/866b81a8384cce4f24867baca2e6820c.png)
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7 . 椭圆
,已知
、
、
、
中恰有三个点在椭圆
上,圆
的切线
与椭圆
相交于
、
两点,与
轴交于点
,
和
的面积分别为
和
.(O是坐标原点)
(1)求椭圆
的标准方程;
(2)若
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/50e48d1edbfb6a5a48f9a95551d1dbc2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e29b9f30c5e3b95ebf633e079121563.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/22400cdc6abcb8420d80a7bfeb530336.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d72babd92b33b44fa45d0d559c03f617.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bfc3e47a358860345e74450ce2af9f9e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70b1cb1359bcb061ce7737fb7e1b34f1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fc5bd66dd6d5e09ff0893a938aed56e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.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/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e7c8561afa0f1454ea382a625d000a18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e097c8d4c948de063796bd19f85b3a9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e0bd63f55069a3bc870915010b39225.png)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29a3bb07e594e01412d6ae0cff9a11e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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8 . 如图,某市有相交于点
的一条东西走向的公路
与一条南北走向的公路
,有一商城
的部分边界是椭圆的四分之一,这两条公路为椭圆的对称轴,椭圆的长半轴长为2,短半轴长为1(单位:千米).根据市民建议,欲新建一条公路
,点
,
分别在公路
,
上,且要求
与椭圆形商城
相切,当公路
长最短时,
的长为( )
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854684129165312/2856282149724160/STEM/d118b280-0731-4e98-a812-561d973fb3bd.png?resizew=278)
![](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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.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/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9f0009063fe00277645aff1be6e32471.png)
![](https://img.xkw.com/dksih/QBM/2021/11/19/2854684129165312/2856282149724160/STEM/d118b280-0731-4e98-a812-561d973fb3bd.png?resizew=278)
A.![]() | B.![]() | C.![]() | D.![]() |
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2021-11-22更新
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2卷引用:浙江省湖州市三贤联盟2021-2022学年高二上学期期中联考数学试题
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解题方法
9 . 如图,椭圆
的离心率为
且经过点
.
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852633527967744/2856636691734528/STEM/62e2891daeb54addba0ddfe0a8246e42.png?resizew=239)
(1)求椭圆
的方程;
(2)已知圆:
,过点
作圆
的切线
,交椭圆于另一个点
,求
的面积最大值,并求出此时圆的半径
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/851a5d6ec23256f9b4a9e98aa92945fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1b6f209d1a805437046ca6ef79dd.png)
![](https://img.xkw.com/dksih/QBM/2021/11/16/2852633527967744/2856636691734528/STEM/62e2891daeb54addba0ddfe0a8246e42.png?resizew=239)
(1)求椭圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知圆:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a253dc0b555dc304653876d8fe9796c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/532d9de08698f61d7c010805c61a4ec5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/11bc05f41215f9894e11d1df0465751a.png)
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10 . 如果方程
表示焦点在y轴上的椭圆,那么实数k的取值范围是_______________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1db1e7af6d2b0ae5873b4494739fc86c.png)
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