1 . 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,曲线
的极坐标方程为
.
(1)求曲线
的普通方程和曲线
的直角坐标方程;
(2)判断曲线
和曲线
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61bf8382295d2004e865ed8986175eb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f34ad37ee24b2a380d2310c54316067.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b227b38b45b5fce63a6bdad8adf113.png)
(2)判断曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2b227b38b45b5fce63a6bdad8adf113.png)
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名校
解题方法
2 . 若直线的参数方程为
(t为参数),则直线的斜率为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/423941a5bfab3ea68b6783ab9c204a9d.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 直线
:
与曲线
:
(
为参数)相交所得的弦长是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d77f5191798242b7b9b88a75e17e4425.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4420c7c24162d8593064cd51c208d226.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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解题方法
4 . 直线
与
轴分别交于
两点,
是曲线
(
为参数)上的动点,则
面积的最大值是( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcefd18333f55a3aa65c444d68feed1b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b0fffbec1fe851795dfdd448bf0d165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44bc7009f5cbeedefc9f23bf64f8db55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8b17f20c25bb16153b5f2d25062ed7a7.png)
A.![]() | B.![]() | C.![]() | D.2 |
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5 . 在直角坐标系
中,以坐标原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
,
(1)将
的极坐标方程化为直角坐标方程;
(2)设
点的直角坐标为
,
为
上的动点,点
满足
,写出
的轨迹
的参数方程,判断
与
是否有公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/2599c2c6295c4416838931603ca1f6f3.png)
(1)将
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fcabe99e81e2cc46dfcdcada03463a76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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6 . 在平面直角坐标系
中,直线l的参数方程为
(t为参数).以坐标原点O为极点,x轴的正半轴为极轴,建立极坐标系,曲线C的极坐标方程为
.
(1)求直线l和曲线C的直角坐标方程;
(2)若点P为曲线C上任意一点,求点P到直线l的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6ec27872ee205f7f6a6e62e60aadea37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff0d5750d9f747aa93f12a0408672cac.png)
(1)求直线l和曲线C的直角坐标方程;
(2)若点P为曲线C上任意一点,求点P到直线l的距离的最大值.
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2021-01-17更新
|
343次组卷
|
6卷引用:广西河池市2020-2021学年高三上学期期末数学(理)试题
7 . 在直角坐标系
中,曲线
的参数方程为:
(
为参数),曲线
与坐标轴交于(异于坐标原点
)两点
,
.
(1)求线段
的长度;
(2)以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,已知点
,
关于直线
对称,求直线
的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e94cbbb0ef83f59e995f05c466c405.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)求线段
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
(2)以坐标原点
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2020-11-06更新
|
479次组卷
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3卷引用:广西南宁市普通高中2021届高三10月摸底测试数学(文)试题
广西南宁市普通高中2021届高三10月摸底测试数学(文)试题广西南宁市普通高中2021届高三10月摸底测试数学(理)试题(已下线)专题08 平面解析几何-【备战高考】2021年高三数学高考复习刷题宝典(解答题专练)
2013·辽宁沈阳·一模
名校
解题方法
8 . 已知极坐标系的极点在直角坐标系的原点处,极轴与
轴非负半轴重合,直线
的参数方程为:
为参数),曲线
的极坐标方程为:
.
(1)写出曲线
的直角坐标方程和直线
的普通方程;
(2)设直线
与曲线
相交于
两点,求
的值.
![](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/e54655a6e1789716620e602a6cc9daf7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6bce3d91ca23b86d8c6625f2632e437.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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2016-12-02更新
|
2129次组卷
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10卷引用:广西兴安县第二中学2022届高三上学期12月月考数学(文)试题
广西兴安县第二中学2022届高三上学期12月月考数学(文)试题广西兴安县第二中学2022届高三上学期12月月考数学(理)试题(已下线)2013届辽宁省沈阳市第二十中学高三高考领航考试(四)文科数学试卷(已下线)2013-2014年吉林省长春市十一中高二下学期期末考试理科数学试卷(已下线)2013-2014年吉林省长春市十一中高二下学期期末考试文科数学试卷2017届河北衡水中学高三摸底联考(全国卷)数学(理)试卷2017届河北衡水中学高三摸底联考(全国卷)数学(文)试卷2017届江西省上饶市高三第一次模拟考试文数试卷1江西省吉安市新干县第二中学2018届高三上学期第一次月考(文)数学试题江西省宜春市丰城中学2023届高三上学期入学考试数学(文)试题
9 . 已知曲线的参数方程为:
(
为参数,
),点
为其图象上的一点,若
点的横坐标为2,则点
的纵坐标为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a5461e6bfa77dbdb8ea0add650dbeb8d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8eec3e684af41f9ed4db5b931b9ccfb6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ce066003c0a1f0879cbca2f32802e9b.png)
A.![]() | B.![]() ![]() | C.![]() | D.![]() |
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10 . 设
,
分别为曲线
:
(
为参数)与直线
:
上的动点,则
的最小值为______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f721c6826fbf8a36946347768b722de.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/c380567212748bedfb1955b6ca961155.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d44e8bc37ed03f44470762748a8f942a.png)
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