1 . 在直角坐标系
中,曲线
的普通方程为
,以
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)若点
为曲线
上的动点,
,
,求
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/f8d6101f73518c2cc5c1ab9c5a89dfab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1fcf82d01c39fd2c96e1edba0ad37dd6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a430c41f782c5c12f68a49c5d0cb1ee2.png)
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解题方法
2 . 曲线C的方程为
,把曲线
上所有点的横坐标变为原来的
,再向上平移1个单位,得到曲线E,
是曲线E上的动点.
(1)求曲线E的方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
(1)求曲线E的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
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2021-11-27更新
|
422次组卷
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2卷引用:江西省南昌市八一中学、洪都中学等4校2021-2022学年高二上学期期中联考数学(理)试题
名校
3 . 已知曲线C的极坐标方程为
.
(1)若直线
过原点,且被曲线C截得弦长最短,求此时直线
的标准形式的参数方程;
(2)
是曲线C上的动点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4ac1231479c8318f24ceb879072e32.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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4 . 在平面直角坐标系
中,圆
的圆心为
,半径为
,现以原点为极点,
轴的正半轴为极轴建立极坐标系.
(1)求圆
的极坐标方程和一个参数方程;
(2)设
、
是圆
上两个动点,且满足
,求
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/7160d93f92089ef36f3dab809d3114b8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bdaa19de263700a15fcf213d64a8cd57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ad737cc531c7af1fe36eba567e5d2e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c828c44a61d2eca627dd4fd96f3cedb6.png)
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2021-10-06更新
|
856次组卷
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3卷引用:英才大联考2022届高三上学期月考试卷二文科数学(全国卷)试题
5 . 在直角坐标系
中,曲线
的普通方程为
,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
.
(1)求直线
的直角坐标方程,并写出曲线
的一个参数方程;
(2)已知
是曲线
上的点,求点
到直线
的距离的最小值.
![](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/27f642cc82f9cb94f68265b4ec78f8c2.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/fcfc977fedf0114ed25f65369c871cf8.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2021-10-03更新
|
460次组卷
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2卷引用:百师联盟2022届高三一轮复习联考(一)(全国1卷)文科数学试题
名校
6 . 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)求
的直角坐标方程;
(2)设点
的直角坐标为
,点
的直角坐标为
,动点
满足
,求点
的轨迹
的参数方程,并判断
与
的位置关系.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/84a91cb8d2b89d64fa45c1f2df82e969.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/76fcc6232011aa26602c18f33468a868.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbabae3549b4c67c5fcbd60e0a6d7519.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9cfe541293cab8a9a37d23b16ad7577e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
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2021-09-13更新
|
360次组卷
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2卷引用:全国2022届高三第一次学业质量联合检测理科数学(老高考)试题
7 . 在平面直角坐标系
中,已知曲线
:
,以平面直角坐标系
的原点
为极点,
轴正半轴为极轴,取相同的单位长度建立极坐标系.已知直线
:
.
(1)试写出直线
的直角坐标方程和曲线
的参数方程;
(2)在曲线
上求一点
到直线
的最大距离.
![](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/3c190e8bb81a4d26cf638ed246193cc9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/f153e872cb28d3b8d9bf721f0b0fe21f.png)
(1)试写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)在曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
8 . 在极坐标系中,曲线
的极坐标方程为
,以极点为坐标原点
,极轴所在直线为
轴,建立平面直角坐标系.
(1)求曲线
的参数方程;
(2)若
,
是曲线
上两点,
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6e917503b394fe3e4086b3f8f6f1a13f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6fdd9d94cd1a2d84173eeed5983918c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f7b8cf916f5b1d17ae2e4865f7caef63.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c567bb4b7f272e3fb1839d4edaea1f6f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ede7ef59121690ed3fdb4e6a764b7e09.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2de7abc1c27897e27c4e3086f2bb6d8f.png)
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2021-07-09更新
|
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2卷引用:江西省六校2020-2021学年高二下学期期中联考数学(文)试题
解题方法
9 . 以抛物线
的焦点为圆心,且与直线
(
为参数)相切的圆的标准方程是____________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e48f28aeccf369df5980ac787e9e313f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5829f2f79ee68223117f3d9d85a9fff2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2021-07-08更新
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1340次组卷
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7卷引用:2021年江苏省普通高考对口单招文化统考数学试题
2021年江苏省普通高考对口单招文化统考数学试题(已下线)专题11 坐标系与参数方程-2021年高考真题和模拟题数学(文)分项汇编(全国通用)(已下线)专题11 坐标系与参数方程-五年(2017-2021)高考数学真题分项汇编(文科+理科)(已下线)考点03 抛物线-2022年高考数学(文)一轮复习小题多维练(全国通用)(已下线)考向26 圆与方程-备战2022年高考数学一轮复习考点微专题(上海专用)(已下线)第56讲 参数方程(讲) — 2022年高考数学一轮复习讲练测(课标全国版)(已下线)文科数学-2022年高考考前20天终极冲刺攻略(三)
名校
10 . 在平面直角坐标系
中,以坐标原点
为极点,
轴的非负半轴为极轴且取相同的单位长度建立极坐标系,已知曲线
的极坐标方程为
;直线
的倾斜角为
,且
经过曲线
的左顶点.
(1)求曲线
的直角坐标方程和直线
的参数方程;
(2)求曲线
的内接矩形
的周长的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/55d7ff3dff3185177229e8e356a18762.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3b199d124fb9a5bc8438c9884f04534.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
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2021-06-22更新
|
517次组卷
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2卷引用:河南省郑州市2020-2021学年高二下学期期末数学文科试题