1 . 在平面直角坐标系上,已知点
,
,
是平面上的一个动点,设
,
,满足
.
(1)求
的取值范围;
(2)求点
的轨迹,并画出它的图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913f78382630e50543e5f7192cae3ed3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/654159e5670167bd400ad8bf02d57632.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2428a66ef7d3a2325fd3e74a0997a61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/58b0ba5c937b27a27b5ef5ab9e51a935.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(2)求点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
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2 . 如图,正
的边长为1,
分别是边
上的点,将三角形沿
对折,顶点
恰好落在边
上的点
处,设
,求
满足的关系式并在直角坐标系中画出大致图像,求出
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9178fc8b5d65aa75fa9196294a0db7e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/98842968c75427c940b34de391a3a778.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/62c6f95fb0f50d816861bc3a526aee76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1a6c6e7c025362c46a64a8956761f08e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/764509115979e9958101808383672ec0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f4e89e2468f74be03fd14c62e1a157e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9defa23d2a9b88f4dd10e0ea4bef2189.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/16/e4bfcfd8-40db-489f-9b73-4bc66ef9e712.png?resizew=155)
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3 . (1)画出函数
的图像;
(2)如果关于
的方程
有4个实数根,求实数
的取值的集合.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e0b18ec602912fdf62a780813e969d58.png)
(2)如果关于
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8004926535d4be0db722094317b9ca4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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4 . 如图,A为x轴正半轴上一点,
; B为ON上的一点,且
;C为AB的中点,且关于OB的对称点为D.求点D的轨迹方程,并画出大致图像.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cc6ce1a7febc2efc0267a9703cb028c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0e7fa3aea72ccc36948a4a90f7368f71.png)
![](https://img.xkw.com/dksih/QBM/2018/12/4/2089400111366144/null/STEM/1f0876bbb2364d1e9731aaa003e9b722.png?resizew=395)
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