1 . 以等边三角形的每个顶点为圆心,以其边长为半径,在另两个顶点间作一段圆弧,三段圆弧围成的曲边三角形被称为勒洛三角形,如图,在极坐标系
中,曲边三角形
为勒洛三角形,且
,
,以极点O为直角坐标原点,极轴
为x轴正半轴建立平面直角坐标系
,曲线
的参数方程为
(t为参数).
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340809728/STEM/d3758e8d-6d89-4964-afcf-baefe35bb3a9.png?resizew=155)
(1)求
的极坐标方程和
所在圆
的直角坐标方程;
(2)已知点M的直角坐标为
,曲线
和圆
相交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd6c71a0da6a878a5b12bf8a8e784645.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aff004ccf61c3ae95d7f8183cd9740b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a480ba768f87a78e40d443962478f11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](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/363f54a5b060e52de378316767920562.png)
![](https://img.xkw.com/dksih/QBM/2022/6/2/2992613741322240/2995556340809728/STEM/d3758e8d-6d89-4964-afcf-baefe35bb3a9.png?resizew=155)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5a6b11637ea396e989ab32d780e745b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320c0f9263761963de27e41442a62a42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知点M的直角坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/edaef66a0582e95fb5c57a405acdea9a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/187663c963598cd7b5ce79d80faac37f.png)
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2022-06-06更新
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6卷引用:吉林省吉林市普通高中2022届高三第四次调研测试理科数学试题
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