真题
1 . 已知L为过点
倾斜角为
的直线,圆C为中心在坐标原点而半径等于1的圆,Q表示顶点在原点而焦点在
的抛物线.设A为L和C在第三象限的交点,B为C和Q在第四象限的交点.
(1)写出直线L、圆C和抛物线Q的方程,并作草图;
(2)写出线段
、圆弧
和抛物线上
一段的函数表达式;
(3)设
依次为从P、B到x轴的垂足,求由圆弧
和直线段
所包含的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5e1b47facc92d3733641ac44beaa9a59.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af80af0bc8a85523e29b5ed18ab701d8.png)
(1)写出直线L、圆C和抛物线Q的方程,并作草图;
(2)写出线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b90e0f35eda1a729fed485f83da5ea9d.png)
(3)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/802fe32b0d11aa1f5e172396e47cd75e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6f9ccd6d033f7009c1c3619b016e2e22.png)
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