1 . 如图是以等边三角形
的每个顶点为圆心,以边长为半径,在另两个顶点间作一段弧,三段弧围城的曲边三角形,记为勒洛
(勒洛三角形是德国机械工程专家,机构运动学家勒洛首先发现的,故命名为勒洛三角形).在平面直角坐标系
中,以坐标原点O为极点,以x为轴正半轴为极轴建立极坐标系,(规定:极径
,极角
),已知点
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e70268de-beca-4f44-8f5b-1a2c749a3963.png?resizew=193)
(1)求
和
的极坐标方程;
(2)已知点
,Q是
上的动点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fe95f656b98b53f71a9d72bf0c9a4b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/278949a1dbbe742ef4dfb4596fd94911.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c190373ee81d43a2f12f2482e8977680.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f299452d466df7bc11c761c3d2d037f9.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/8/e70268de-beca-4f44-8f5b-1a2c749a3963.png?resizew=193)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f606bf7959544f92f299b27053041e85.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7500f8e5d957a762f4738fcb6e1af18d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16d65cecaf8a3dc2953f4109c75a981e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33f077fb4f73c2123538e19365d84748.png)
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