1 . 若复数
的实部为4,则点
的轨迹是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/296ff2a951b1289afab987fadb46f43f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/82a79a33a83a7ba57a34b5093d1d1d02.png)
A.短轴长为4的椭圆 | B.实轴长为4的双曲线 |
C.长轴长为4的椭圆 | D.虚轴长为4的双曲线 |
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2024-04-24更新
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3卷引用:四川省雅安市2024届高三下学期4月联考数学(理)试题
2 . 平面直角坐标系中,等边
的边长为2,M为
中点,B,C分别在射线
,
上运动,记M的轨迹为
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79301e3963cf05b1ac7c249749420475.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 已知
的两个顶点
的坐标分别是
,且
所在直线的斜率之积等于
,则( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c6917df35ab960d5958af89095219434.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e675a92cad72c65aa4071b9d9e226090.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87484a879f450ab097f720fb2a0f4a2f.png)
A.当![]() ![]() ![]() ![]() |
B.当![]() ![]() ![]() ![]() |
C.当![]() ![]() ![]() ![]() |
D.当![]() ![]() ![]() ![]() |
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2024-02-04更新
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2卷引用:山东省枣庄市2024届高三上学期期末数学试题
4 . 希腊数学家帕普斯在他的著作《数学汇篇》中,完善了欧几里得关于圆锥曲线的统一定义,并对这一定义进行了证明,他指出,到定点的距离与到定直线的距离的比是常数
的点的轨迹叫做圆锥曲线:当
时,轨迹为椭圆;当
时,轨迹为抛物线;当
时,轨迹为双曲线,则方程
表示的圆锥曲线为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/168b3e4b1d6f04226fa2687a72a268b4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/42b7ac29311c13aa538f3f48cb513b0d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/09dbcaa127022fbd6b6f13345196408a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a58c44592477e5cab15cd165ff9b3d78.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd04d1e6c67aa5a825f578f05742a5e2.png)
A.椭圆 | B.双曲线 | C.抛物线 | D.以上都不对 |
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2024-01-27更新
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356次组卷
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2卷引用:黑龙江省龙东地区五校2023-2024学年高二上学期期末联考数学试卷
5 . 曲线
是平面内与三个定点
,
和
的距离的和等于
的点的轨迹.给出下列四个结论:
①曲线
关于
轴、
轴均对称;
②曲线
上存在点
,使得
;
③若点
在曲线
上,则
的面积最大值是1;
④曲线
上存在点
,使得
为钝角.
其中所有正确结论的序号是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b9bece414af7ecb2d796dc8a6f549e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27e62a44b8712ce4483b8710cda0dc1c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/06549cb7ea8b88dd5eb2e3d5a2ca7828.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/95bacae35b6e16a0a33c2bdc6bc07df7.png)
①曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
②曲线
![](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/534cea1167e2a081fa814a652a4c7fba.png)
③若点
![](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/002ed1ebb2cb936e10ab478789f91c7c.png)
④曲线
![](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/c94fe48bf7af022ecbbe13833fdcc2c8.png)
其中所有正确结论的序号是( )
A.②③④ | B.②③ | C.③④ | D.①②③④ |
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2024-01-25更新
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5卷引用:四川省成都市石室中学2024届高三上学期期末数学(理)试题
6 . 如果点
在运动过程中,总满足关系式
,那么点
的轨迹为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/266ed8002a339746965afc42d6ba1dec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
A.椭圆 | B.直线 | C.线段 | D.圆 |
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解题方法
7 . 如图,在圆
(
)上任取一点
,过点
作
轴的垂线段
,
为垂足.当点
在圆上运动时,线段
的中点
的轨迹是椭圆,那么这个椭圆的离心率是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3503d330608e7138d1b529aba4512fa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0629ce42392a7fe9be21d25c39c3e64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2024/1/9/5e38e829-bc1d-486c-9d1b-d58922dc00ab.png?resizew=157)
A.![]() | B.![]() |
C.![]() | D.![]() |
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2024-01-11更新
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3卷引用:江苏省2023-2024学年高二上学期期末迎考数学试题(B卷)
解题方法
8 . 如图,长为a(a是正常数)的线段AB的两个端点A,B分别在互相垂直的两条直线上滑动,点M是线段AB上靠近A的三等分点,则下列说法正确的为( )
A.点M的轨迹是圆 | B.点M的轨迹是椭圆且离心率为![]() |
C.点M的轨迹是椭圆且离心率大小与a有关 | D.点M的轨迹不能确定 |
您最近一年使用:0次
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解题方法
9 . 已知曲线
的方程为:
,点
,
的坐标分别为
,
,过点
的直线交曲线
于
,
两点,且
,
,
三点不共线,则
的周长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a83a03933e1edf5e912243c3c33cc795.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/f9c59f0e35b7ae5206e45878934482b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2fb6fd712d967a36c027693a54f91470.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.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/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/661ff55b5ebbadfb600989af3cfce2fd.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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10 . 定义一个对应法则
(
,
),比如
.已知点
和点
,
是线段
上的动点,点
在法则
下的对应点为
.当
在线段
上运动时,点
的轨迹为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4cad68964aac236c9202d17c543dc53.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/be466586da8810ccfd811c59a747adb8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b6c5526947e9bef051bc3bdf7fd186d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac68f17ee741f6df7b807bfadce39f88.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a42952b85622c1c5e461905c3278eee4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2db781b1a23c37498863885763324e9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca4ff0af96ea467337cb30c4c765b5f7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da895d8bd043625a0839128252130d9.png)
A.线段 | B.圆的一部分 | C.椭圆的一部分 | D.双曲线的一部分 |
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