1 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),在以坐标原点
为极点,
轴正半轴为极轴的极坐标系中,直线
的极坐标方程为
.
(1)求曲线
的普通方程与直线
的直角坐标方程;
(2)过原点且倾斜角为锐角的直线与曲线
,直线
分别交于
两点,且
,求该倾斜角的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd383b772a2b72a1ca12148eaa852f6b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](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/757cc2f991fc97a773ceffbbd3a041fa.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过原点且倾斜角为锐角的直线与曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c625d16a884aa69c757f2aece677ae50.png)
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解题方法
2 . 已知直线![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995d537587c94c8bd1420659a500babf.png)
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,圆
的极坐标方程为
,圆
与极轴和直线
分别交于点
,点
(异于坐标原点).
(1)写出点
的极坐标及圆
的参数方程;
(2)求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/995d537587c94c8bd1420659a500babf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4eb989ab123acd2b26f7734444a3715d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1b6d2853ae57f4d2c3b5a0ac6fd4a5f.png)
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/120c0192f3a2e1bf69348350a710b737.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)写出点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1180d78cdefd8c9fce9ba57d16fb774e.png)
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3 . 如果圆
上任意一点
都能使
成立,那么实数
的取值范围是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0715c6a0919ed27093092ec21250fc66.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/28965097a2c8f6872accc5ba80f44dfd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c3b2be668406c687a3144761731eb1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/071a7e733d466949ac935b4b8ee8d183.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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7卷引用:广西钦州市第一中学2021届高三开学摸底考试数学(文)试题
广西钦州市第一中学2021届高三开学摸底考试数学(文)试题内蒙古乌兰察布市集宁一中2017-2018学年高一下学期第二次月考数学(理)试题【全国百强校】四川省雅安中学2019届高三上学期开学考试数学(文)试题山西省朔州市怀仁县大地学校2019-2020学年高二下学期期末文科数学试题山西省朔州市怀仁县大地学校2019-2020学年高二下学期期末理科数学试题(已下线)调研测试四(A卷 基础过关检测)-2021年高考数学(文)一轮复习单元滚动双测卷(已下线)第01讲 两角和与差的三角函数-【帮课堂】2021-2022学年高一数学同步精品讲义(苏教版2019必修第二册)
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4 . 在直角坐标系xOy中,曲线C的参数方程为
为参数
以坐标原点为极点,以x轴的正半轴为极轴,建立极坐标系.
写出曲线C的极坐标方程;
设点M的极坐标为
,过点M的直线l与曲线C相交于A,B两点,若
,求AB的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7943ed5542e16cbe7b722248051c907b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a999fda5febcf29a602dc236e5f65de2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4141b26d2c32655003494a91ad6331b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65863c1abad833b79c303bfca24f535c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/33119a0a14e6493a0debfc09c37f856a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f36de56e1e8f0bae0b7efbcc3b4a864d.png)
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2018-09-10更新
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9卷引用:广西崇左高级中学2020-2021学年高二下学期第一次月考数学(理)试题
广西崇左高级中学2020-2021学年高二下学期第一次月考数学(理)试题山西省康杰中学2016-2017学年高二下学期期末考试数学(理)试题河北省临漳县第一中学2017-2018学年高二下学期第三次月考数学(理)试题山西省永济中学2018-2019高二下学期期末考试数学(理)试题重庆市第一中学2019-2020学年高三下学期3月月考数学(理)试题2019届安徽省合肥市第一中学高三下学期冲刺高考最后一次模拟数学(文)试题2020届宁夏六盘山高级中学高三下学期第二次模拟考试数学(理)试题陕西省西安中学2020届高三下学期第八次模拟考试数学(文)试题西藏林芝市第二高级中学2019-2020学年高二下学期第一学段考试(期中)数学(理)试题
5 . 下列点不在直线
(
为参数)上的是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc38d0ca0fb5a7168550239315d056e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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6 . 在平面直角坐标系xoy中,曲线C的参数方程是
(θ为参数).以坐标原点O为极点,x轴正半轴为极轴,建立极坐标系,直线l的极坐标方程为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edb397059118f5cd68932985d7f98c1.png)
(1)求曲线C的极坐标方程;
(2)设直线θ=
与直线l交于点M,与曲线C交于P,Q两点,已知|OM||OP||OQ|=10,求t的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67b9bf0eb6246a31295503b959471b5f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edb397059118f5cd68932985d7f98c1.png)
(1)求曲线C的极坐标方程;
(2)设直线θ=
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a9bec2fd3becbbe4a29ebbc00234622f.png)
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7 . 过原点作圆
(
为参数)的两条切线,则这两条切线所成的锐角为_________________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dde1f282dc5c1154170d85b4b8e11e10.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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8 . 在直角坐标系
中,直线
(
为参数)与曲线
(
为参数)相交于不同的两点
,
.
(1)当
时,求直线
与曲线
的普通方程;
(2)若
,其中
,求直线
的倾斜角.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9ca0a5ffac99c52e88e25c303e33ff1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/97bb8a6dfaf12c637ec74b64b9d0f3aa.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4120436d6ff0c58109473edc068257c3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fee8deb17a070d74990762adeba80659.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/317ebedfc0f5a96937fad87914a6f74b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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解题方法
9 . 直线
(t为参数)被圆
所截得的弦长为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04b106b3372456901217e1b2586c3da6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/075115a5bc60e9eae149cfae175994fc.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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4卷引用:广西崇左高级中学2020-2021学年高二下学期期中考试数学(理)试题
10 . 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,
轴正半轴为极轴建立极坐标系,直线
的极坐标方程为
.若直线
与曲线
相切.
(1)求曲线
的极坐标方程;
(2)在曲线
上任取两点
,
,该两点与原点
构成
,且满足
,求
面积的最大值.
![](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/66abdc4d36970d80064fd74baf68ba1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ba6b6aa6c3f9faba6b03bc193a6e61.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](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/0b34c92e08a689132abfa956b7b4400a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd0efc142e3abb0d8f21e6447f0a7a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7519878b8bcbd7a9024167e8abbcacb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d9cd0efc142e3abb0d8f21e6447f0a7a.png)
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2019-04-01更新
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