1 . 已知曲线
,
,给出下列四个命题:
①曲线
关于
轴、
轴和原点对称;
②当
时,曲线
,
共有四个交点;
③当
时,曲线
围成的区域内(含边界)两点之间的距离的最大值是3;
④当
时,曲线
围成的区域面积大于曲线
围成的区域面积.
其中所有真命题的序号是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/282c73aa06e789c79766977e9b278b6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/407bdf4be5d3319d0cd89c1863251928.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
③当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e94f16d5ed858699bfea5039a7bf8ae6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
④当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe9e329f2730b2be926b121f1ae04c0f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
其中所有真命题的序号是
您最近一年使用:0次
名校
2 . 已知曲线
:
,
:
,中
.①当
时,曲线
与
有
个公共点;②当
时,第一象限内,曲线
位于曲线
的下方;③存在实数
,使得曲线
围成的区域面积恰等于
围成的区域面积;④曲线
围成的区域内(不含边界)的整点(即横、纵坐标均为整数的点)的个数不多于曲线
围成的区域内(不含边界)的整点的个数.其中,所有正确结论的序号是________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00b39b780f6d0055f581651235371d94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b98b1a0de7be943883e5a07a01899f33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b140e221ddf537b8964fff8557cca0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf0086b054ef120408acac806a1b1318.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8860d9787671b53b1ab68b3d526f5ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4875f6b13d20d1389a26ad77cca5bd00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e23f593cd4b055a3f6b0705cd70a99e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c3ff0b0fea1cb642d3f6be77a1ff32f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a6eaa137a2290a9a9ec7ad635d17dbb6.png)
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3 . 中国结是一种手工编织工艺品,因为其外观对称精致,可以代表汉族悠久的历史,符合中国传统装饰的习俗和审美观念,故命名为中国结,中国结的意义在于它所显示的情致与智慧正是汉族古老文明中的一个侧面,也是数学奥秘的游戏呈现.它有着复杂曼妙的曲线,却可以还原成最单纯的二维线条,其中的八字结对应着数学曲线中的双组线.曲线
是双纽线,则下列结论错误的是( )
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/9d7e1f87-d135-4379-9a7b-457a02f04b73.png?resizew=205)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcaa11ca27192e769327981ba4f34c06.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/3/1/9d7e1f87-d135-4379-9a7b-457a02f04b73.png?resizew=205)
A.曲线C的图象关于原点对称 |
B.曲线C经过5个整点(横、纵坐标均为整数的点) |
C.曲线C上任意一点到坐标原点O的距离都不超过3 |
D.若直线![]() ![]() |
您最近一年使用:0次
名校
解题方法
4 . 已知
是椭圆
与抛物线
的一个共同焦点,
与
相交于A,B两点,则线段AB的长等于( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6533a2123bcaa8c7dcd36d5e3f37700f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0107aa23cf707446f947fa236421c1f0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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2022-12-15更新
|
1060次组卷
|
6卷引用:上海市嘉定区第一中学2024届高三上学期开学考试数学试题
上海市嘉定区第一中学2024届高三上学期开学考试数学试题上海市虹口区2023届高考一模数学试题(已下线)专题9-1 圆锥曲线(选填)-3(已下线)模块六 平面解析几何-2(已下线)核心考点03椭圆与双曲线(1)上海市闵行中学2024届高三上学期10月月考数学试题
名校
解题方法
5 . 如图,椭圆
、双曲线
中心为坐标原点
,焦点在
轴上,且有相同的顶点
,
,
的焦点为
,
,
的焦点为
,
,点
,
,
,
,
恰为线段
的六等分点,我们把
和
合成为曲线
,已知
的长轴长为4.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/497d2ab5-76f7-4b22-a913-4f322710db9d.png?resizew=243)
(1)求曲线
的方程;
(2)若
为
上一动点,
为定点,求
的最小值;
(3)若直线
过点
,与
交于
,
两点,与
交于
,
两点,点
、
位于同一象限,且直线
,求直线
的方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.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/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/522230546d4b802094e86ceb48c2ba38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b4f150ab98bde511e0f65d9bafab031.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a18722354086c42e62334983fc50eb6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd3b9e816b14051f785aa5aae72b8eed.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa379773b0244afedf8d855a42838d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/2/10/497d2ab5-76f7-4b22-a913-4f322710db9d.png?resizew=243)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bcd8ee2d8367c167d6ae0abc741b6b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/57502a580c6aee9992af061073855e06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c8dbe91bd8e17a077ddb7d3ba2e12c8.png)
(3)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce30fc0664cca88dbe6d38f32aee81e6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9cb8e6ff801523b0304576cd69fd2d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaafb050b24c4e806c480e0665aaa5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eae863e7a1f1fed09f1075de4a817c63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2708fa6298e52f617383efc175b71ddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a86380a6d6501f6504dcb4aa5e3099f2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/577621d5b3d1ddd683ce96e96b0d004f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-02-09更新
|
643次组卷
|
4卷引用:新疆乌鲁木齐市第101中学2022-2023学年高二下学期开学考试数学试题
名校
解题方法
6 . 对于椭圆
,定义双曲线
为其伴随双曲线,则下列说法中正确的有( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd486b8796b3454eab219c28ed131683.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c5c2e64358e0ec7aa142c336d970306.png)
A.椭圆![]() ![]() |
B.若椭圆![]() ![]() ![]() ![]() ![]() |
C.若椭圆![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
D.若椭圆![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
您最近一年使用:0次
2022-03-05更新
|
719次组卷
|
3卷引用:江苏省扬州市2021-2022学年高二下学期期初调研测试数学试题
江苏省扬州市2021-2022学年高二下学期期初调研测试数学试题江苏省泰州中学2023-2024学年高二上学期第二次质量检测数学试题(已下线)第三章 圆锥曲线的方程(压轴必刷30题7种题型专项训练)-【满分全攻略】2023-2024学年高二数学同步讲义全优学案(人教A版2019选择性必修第一册)
名校
解题方法
7 . 已知圆
与抛物线
相交于点
,
,
,
,且在四边形
中,
.
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848908578332672/2849264380796928/STEM/67a86025e398470c9902f7c282e47d69.png?resizew=227)
(1)若
,求实数
的值;
(2)设
与
相交于点
,
与
组成蝶形的面积为
,求点
的坐标及
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/519d5dfc27226492c7003c73534624bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4bb9757015d815d02e8e99f2475ce3e3.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f79863ffcfa63117ca6741b20a48e69.png)
![](https://img.xkw.com/dksih/QBM/2021/11/11/2848908578332672/2849264380796928/STEM/67a86025e398470c9902f7c282e47d69.png?resizew=227)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2697bd158b528c992421d24cd7813c4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ef4b54df90e5528f155ab2902a2eea2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ffffbccf0eb96123a237860c12a1b892.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/895dc3dc3a6606ff487a4c4863e18509.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf231f8f86fb922df4ca0c87f044cec3.png)
您最近一年使用:0次
2021-11-11更新
|
357次组卷
|
4卷引用:数学-2022届高三下学期开学摸底考试卷C(新高考专用)
8 . 曲线
与
交点的个数为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad72445eea1da447ae09a123a54608f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/211520616ac6312cc6989c6255982565.png)
A.1 | B.2 | C.3 | D.4 |
您最近一年使用:0次
9 . 在直角坐标系
中,曲线
的参数方程为
(
为参数)以坐标原点为极点,
轴非负半轴为极轴建立极坐标系,且在两坐标系下长度单位相同.曲线
的极坐标方程为
.
(1)当
时,
是什么曲线?
(2)当
时,求
与
的公共点的直角坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67f6b72279cc0f98c8cccf030a4f7216.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/64d50140eeb8dade6083148566fcc73b.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5095a28bb1b91bf6bed9e2cfbd76bb18.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcbd5bb726a08c308b48373afebbb768.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
您最近一年使用:0次
2021-02-24更新
|
525次组卷
|
3卷引用:安徽省皖江名校联盟2021届高三下学期2月开年考理科数学试题
10 . 已知集合
,
,则
( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d4e8b91b04bebec1d952b15f95cdb81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a6a3eae1010a7df35ac217a0622b8e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4b9b470218359a4a47be9244980489e.png)
A.![]() | B.![]() | C.![]() | D.![]() |
您最近一年使用:0次
2020-09-16更新
|
843次组卷
|
8卷引用:四川省成都七中2020-2021学年高三入学考试数学文科试题