名校
1 . 已知心形线是由一个圆上的一个定点,当该圆绕着与其相切且半径相同的另外一个圆周上滚动时,这个定点的轨迹,因为其形状像心的形状而得名.在极坐标系
中,方程
表示的曲线
就是一条心形线,如图,以极轴
所在直线为
轴,极点
为坐标原点的直角坐标系
中,已知曲线
的参数方程为
(
为参数).
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846752386367488/2850540072157184/STEM/2be71326-2d9a-4f3a-84fa-cbfce7132cdc.png)
(1)求曲线
的极坐标方程;
(2)求曲线
与
交点个数.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6c32c6873c5c65beed9a5ab160e14230.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b948d7f23155a7d3c9d23c710f227add.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/2021/11/8/2846752386367488/2850540072157184/STEM/2be71326-2d9a-4f3a-84fa-cbfce7132cdc.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2021-11-13更新
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3卷引用:陕西省宝鸡市陈仓区2022届高三上学期第一次教学质量检测文科数学试题