名校
1 . 在直角坐标系
中,曲线C的参数方程为
(
为参数),直线
的方程为
(
为参数)
(1)若
求曲线C与直线
的交点坐标;
(2)若曲线C上的点到直线
的距离最大值为
求实数
的值;
(3)曲线C与
轴的交点由上至下分别为
P为曲线C上异于
的一动点,若点Q满足:
判断
与
的面积之比是否为定值,若是,求出该定值;若不是,请说明理由.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea0a82ada06ef4019a933ff7c680e0ba.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5da88a192036c3e7e0f8d3960416066.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f3b0a2ead66eac66c32217540f71a86.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)若曲线C上的点到直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53b627c07acf9058dc2000f7e3b48244.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
(3)曲线C与
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d86b64ef9a89f4f1d85a7616df5c7d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b1fd1784f10d8607df59399dbf5d105.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba977cdf41dc862d49f82f2d4ada49af.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ba28fa84592f63779484dd1faef8fa6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/afe4421ae50dcd93b61e7d8b1b7f74f3.png)
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2 . 无论
取任何实数,直线
与椭圆
恒有交点,则实数
的取值范围是_____ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/02ebce8b2a915356ed39f36c5bad2ebe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/314adcacb4b1bfa31a5a7118bcadc175.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
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13-14高三下·上海虹口·阶段练习
名校
3 . 已知极坐标系的极点为直角坐标系的原点
,极轴与
轴的非负半轴重合.若直线
的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3009c4470bcc03fc540440c51c78c830.png)
,曲线
的参数方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd5c8d8bca1171d4c4405f2fdee1c38.png)
为参数,且
,则直线
与曲线
的交点的直角坐标为 .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3009c4470bcc03fc540440c51c78c830.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f7bcd7f83a68755ad2a3f491f7655a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1bd5c8d8bca1171d4c4405f2fdee1c38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb6d15a9057d94e0fa976899553a5e00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/523aa4f813faa2dec0978c6b04c30f00.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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