解题方法
1 . 在直角坐标系
中,曲线C的参数方程为
(
为参数),以坐标原点为极点,x轴正半轴为极轴建立极坐标系,已知直线l的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
.
(1)写出C的普通方程;
(2)写出直线l的直角坐标方程并判断l与C有无交点,如果有,则求出交点的直角坐标;如果没有,写出证明过程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1e01f56efc66780e4bf66dc39f12fb27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b04652e01c3aecccc2d5053af869a657.png)
(1)写出C的普通方程;
(2)写出直线l的直角坐标方程并判断l与C有无交点,如果有,则求出交点的直角坐标;如果没有,写出证明过程.
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2023-05-31更新
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4卷引用:新疆叶城县第六中学2023届高三下学期高考考前最后一次诊断数学试题
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2 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数),以坐标原点
为极点,
轴的正半轴为极轴,取相同长度单位建立极坐标系,直线
的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de16f0a20bc6d505cf707c07c72c1810.png)
(1)求曲线
的普通方程和直线
的直角坐标方程;
(2)设直线
与
轴的交点为
,经过点
的动直线
与曲线
交于不同的
,
两点,证明:
为定值
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce6b587aaa2d40fc143d19de4c70f96c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3217fa687c8a339e86fc482c826e2edf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de16f0a20bc6d505cf707c07c72c1810.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9fcf9bfbf771cb6118f8e631724314e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fc5c19ac440746be97d8b46af5d288a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab4717e4827480f0f6f4ded85e52eab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f7fa8ab7532d8eeb9d8d4657e3d7c53.png)
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2022-10-20更新
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3卷引用:新疆维吾尔自治区喀什第六中学2023届高三上学期9月实用性月考(一)数学(文)试题
3 . 在直角坐标系
中,曲线
的参数方程是
(
为参数),以坐标原点为极点,
轴的正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程;
(2)已知曲线
上两点
,
的极坐标分别为
,
,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f44e1237be15d8bef71d0d33cd9f86e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/618f23cccdba8f7db0687e9f844509ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c640f9de67df348d9586b63eec7eabd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bb149143a2e693abdccd0bb590e51dfb.png)
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5卷引用:新疆喀什第二中学2022届高三11月月考数学试题
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