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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,
轴的正半轴为极轴建立极坐标系,直线
的极坐标方程为
(
为直线
的斜率且
).
(1)将曲线
和直线
化为普通方程;
(2)设曲线
与直线
交于
两点,线段
的中点为
.证明:直线
的斜率与直线
的斜率的乘积为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4e95a3f74853cbdce7d3dc111d08e30b.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/f0d11c0c228e73a4a8399ac63b4fe677.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f0a532e15e232cb4b99a8d4d07c89575.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2c80c26a794a844127aae7dee87c93b.png)
(1)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设曲线
![](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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2 . 在平面直角坐标系中,直线l的参数方程为
(t为参数).以原点为极点,x轴的非负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的极坐标方程和曲线C的直角坐标方程;
(2)设点
,直线l与曲线C交于点A,B.求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d2a007d1b907662a60a19aea86c9b37.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/822ca9ad42ff37f5a00a7c90b1d96d64.png)
(1)求直线l的极坐标方程和曲线C的直角坐标方程;
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88659e1bac79840020d4494440cfb8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25346740294b630c2df2a4ac2857de28.png)
您最近一年使用:0次
2023-03-16更新
|
1010次组卷
|
4卷引用:陕西省延安中学2022-2023学年高二下学期期中文科数学试题
3 . 在极坐标系中,
,
,
,以极点O为原点,极轴为x轴的正半轴,建立平面直角坐标系,已知直线l的参数方程为
(t为参数,
),且点P的直角坐标为
.
(1)求经过O,A,B三点的圆C的极坐标方程;
(2)求证直线l与(1)中的圆C有两个交点M,N,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ea1a9821a00b71f6b7d7a76d91b3f810.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68f2fee11cd80e25b6f319c34eccc4f3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c36e2bbd82360f0411080435c8b4b04.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f1108bdbdc840746ab6c3428e82f6144.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3fa528bcfeca58c46fedfeaf0969d3a4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27cf818dd484cc4cebd40a5f28eb8e9f.png)
(1)求经过O,A,B三点的圆C的极坐标方程;
(2)求证直线l与(1)中的圆C有两个交点M,N,并求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
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名校
4 . 在平面直角坐标系
中,圆C的参数方程为
(
为参数),直线l的参数方程为
(t为参数),设原点O在圆C的内部,直线l与圆C交于M,N两点;以O为极点,x轴的正半轴为极轴建立极坐标系.
(1)求直线l和圆C的极坐标方程,并求a的取值范围;
(2)求证:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/513ab96d9b0704728f0f15c1186a63d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd9f6ea18207d6f880b28ae20fbdf832.png)
(1)求直线l和圆C的极坐标方程,并求a的取值范围;
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4de13a47637548ce5594ed8d64dec0c.png)
您最近一年使用:0次
2022-02-21更新
|
525次组卷
|
3卷引用:陕西省西安中学2022届高三下学期四模理科数学试题
名校
5 . 如图,在直角坐标系中,以原点
为极点,
轴正半轴为极轴建立极坐标系.图中的心型曲线
的极坐标方程为
为曲线
上一动点,曲线
的参数方程为
为参数,
.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/5bd37748-3b01-4e4d-a829-878f30a531b7.png?resizew=155)
(1)若
与
交于
三点,证明:
为定值;
(2)射线
逆时针旋转
后与
交于点
,求
的最大值.
![](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/fe4d6fb3e3916b46c2e544eaaba973d5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e6a3099c2c948513459151da0dce79f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/96b463ed27be664efc447bdc4b4aa936.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/9/30/5bd37748-3b01-4e4d-a829-878f30a531b7.png?resizew=155)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5731a7a079c190e18daa159c67765a41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaf3369e0ea90e8d5cf4b6b3c45c0fd8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5784acc1b6ce159c1193b1581eead14.png)
您最近一年使用:0次
2022-04-07更新
|
725次组卷
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4卷引用:陕西省西安中学2022届高三下学期第五次模拟考试理科数学试题
陕西省西安中学2022届高三下学期第五次模拟考试理科数学试题(已下线)押全国卷(理科)第22题 坐标系与参数方程-备战2022年高考数学(理)临考题号押题(全国卷)黑龙江省大庆市大庆中学2022届高三第二次模拟数学(理)试题江西省宜春市上高二中2022届高三5月第十次月考数学(理)试题
名校
6 . 在平面直角坐标系中,P为曲线
(
为参数)上的动点,将P点纵坐标不变,横坐标变为原来的一半得Q点.记Q点轨迹为
,以坐标原点
为极点,
轴非负半轴为极轴建立极坐标系.
(1)求证:曲线
的极坐标方程为
;
(2)
是曲线
上两点,且
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48f3c9d0427cf88f3b650c59cc6778ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/549ea649efbff82eb432cdcc5cdd73b9.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9faea4deadc69fec42afab055f464340.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/43e651a7faef2db0444fe157613b5779.png)
您最近一年使用:0次
2021-03-06更新
|
1092次组卷
|
3卷引用:陕西省西安中学2021届高三下学期第二次模拟考试数学(文)试题
7 . 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建立极坐标系,若曲线
的极坐标方程为:
.
(1)求曲线
的直角坐标方程;
(2)已知
,过点
作直线
交曲线
于
两点,证明:
为定值.
![](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/f63d6fce5efef48a4e31134cd89179f9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/248909c543977b1a7490bc01fcf44d2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8c552f7bc957eed6b29e76b1b556d2e9.png)
您最近一年使用:0次
2020-09-22更新
|
207次组卷
|
4卷引用:陕西省延安市第一中学2021-2022学年高二下学期第二次月考文科数学试题
8 . 在平面直角坐标系
中,圆
的参数方程为
(
为参数),直线
的参数方程为
(
为参数),设原点
在圆
的内部,直线
与圆
交于
、
两点;以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系.
(1)求直线
和圆
的极坐标方程,并求
的取值范围;
(2)求证:
为定值.
![](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/f6c4a027310e2afbc715fb5ec6cea33f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f8b8876c9b971d4a16429a9019ca9ba2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.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/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/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求直线
![](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/0a6936d370d6a238a608ca56f87198de.png)
(2)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fffd2e3363992060c0b8785f031d2877.png)
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2020-05-30更新
|
954次组卷
|
8卷引用:陕西省汉中市十三校2021-2022学年新高三6月摸底联考理科数学试题
名校
9 . 在平面直角坐标系
中,以坐标原点
为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
,若极坐标系内异于
的三点
,
,
都在曲线
上.
(1)求证:
;
(2)若过
,
两点直线的参数方程为
(
为参数),求四边形
的面积.
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e5094ea2e1ae387f33e0b554c60b14.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9a4aecf3b1ceaa9b4f660030672baddc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a806e583790b07ed766d51249fa013ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a653c31f6db4cfd6b6b2d7bc5a0424b.png)
(2)若过
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8ea6230afeaa1027dc69969cb5d74c3c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5241e0e07a9cd48e4f853405dca1a03.png)
您最近一年使用:0次
2019-04-08更新
|
2892次组卷
|
14卷引用:陕西省西安交通大学附属中学2021届高三下学期第四次模拟考试理科数学试题
陕西省西安交通大学附属中学2021届高三下学期第四次模拟考试理科数学试题【校级联考】江西省吉安一中、九江一中、新余一中等八所重点中学2019届高三4月联考数学(理)试题【校级联考】江西省吉安一中、九江一中、新余一中等八所重点中学2019届高三4月联考数学(文)试题【全国百强校】福建省厦门第一中学2019届高三5月市二检模拟考试数学(理)试题江西省临川二中、临川二中实验学校2019-2020学年高三上学期第三次月考数学(文)试题广东省惠州市2019-2020学年高三第三次调研考试文科数学试题广东省惠州市2019-2020学年高三第三次调研考试理科数学试题(已下线)2020届高三12月第01期(考点13)(文科)-《新题速递·数学》2020届高三1月(考点13-14)(理科)-《新题速递·数学》.广西名校2021届高三大联考(三)数学(文)试题广西桂林、崇左市2021届高三二模数学(理)试题广西桂林、崇左市2021届二模数学(文)试题广西名校2023届高三下学期3月份联考数学(理)试题广西名校2023届高三下学期3月份联考数学(文)试题
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10 . 在极坐标系中,点
坐标是
,曲线
的方程为
;以极点为坐标原点,极轴为
轴的正半轴建立平面直角坐标系,斜率是
的直线
经过点
.
(1)写出直线
的参数方程和曲线
的直角坐标方程;
(2)求证直线
和曲线
相交于两点
、
,并求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5760432cb9dd70e6042d5ac29d506c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2030daf33fd69a0ef6ab1a2dedcc7a33.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acbc6a613224461ade69362d46550474.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
(1)写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求证直线
![](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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13c54cd0878ea19f3ae4d35348c04e7f.png)
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5卷引用:陕西省榆林市子洲中学2020-2021学年高三上学期第一次月考数学(理)试题