1 . 已知在平面直角坐标系xOy中,曲线C的参数方程为
(
为参数
以原点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
.
(1)求曲线和直线的直角坐标方程;
(2)若直线l交曲线C于A,B两点,交x轴于点P,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f9454ffbb2a3834ca8bb61bbf434986b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/913b7537e011acfeec11952731351388.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c8e746aa54acf019ec2c163dadcab3f3.png)
(1)求曲线和直线的直角坐标方程;
(2)若直线l交曲线C于A,B两点,交x轴于点P,求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7384b9afcef2d86a87eee0c66f383052.png)
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2020-12-28更新
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382次组卷
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12卷引用:辽宁省大连市第二十四中学2020届高三6月高考模拟(最后一模)数学(文)试题
辽宁省大连市第二十四中学2020届高三6月高考模拟(最后一模)数学(文)试题辽宁省大连市第二十四中学2020届高三6月高考模拟(最后一模)数学(理)试题2020届湖北省部分省级示范性重点中学教科研协作体高三统一联合考试数学(理)试题四川省绵阳南山中学2020届高三高考仿真模拟热身考试(二)数学(文)试题四川省绵阳南山中学2020届高三高考仿真模拟热身考试(二)数学(理)试题(已下线)专题11 坐标系与参数方程——2020年高考真题和模拟题文科数学分项汇编(已下线)专题12 坐标系与参数方程——2020年高考真题和模拟题理科数学分项汇编(已下线)专题22 坐标系与参数方程-2020年高考数学(理)母题题源解密(全国Ⅱ专版)(已下线)专题22 坐标系与参数方程-2020年高考数学(文)母题题源解密(全国Ⅱ专版)陕西省宝鸡中学2020-2021学年高三上学期月考(二)文科数学试题(A)(已下线)2020年高考全国3数学文高考真题变式题21-23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)
名校
2 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),以原点
为极点,以
轴正半轴为极轴建极坐标系.
(1)求
的极坐标方程;
(2)直线
,
的极坐标方程分别为
,
,直线
与曲线
的交点为
,直线
与曲线
的交点为
,求线段
的长度.
![](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/23367cdea9e6761416b65bc62fceaa7e.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)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cd8754684b9353946fbce47e2b367008.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/366d11e34429b1c54d82177a87300ee6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d158e8f1981b0a07943110f475743fd7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/503233fbd2d032913514f77ab301975d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
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2020-08-05更新
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9卷引用:辽宁省大连市2020届高三下学期第三次模拟考试数学(理)试题
辽宁省大连市2020届高三下学期第三次模拟考试数学(理)试题辽宁省辽阳市2020届高三下学期第三次模拟考试数学(文)试题辽宁省辽阳市2020届高三下学期第三次模拟考试数学(理)试题(已下线)专题11 坐标系与参数方程——2020年高考真题和模拟题文科数学分项汇编(已下线)专题12 坐标系与参数方程——2020年高考真题和模拟题理科数学分项汇编四川省棠湖中学2020-2021学年高三上学期第一次月考数学(理)试题四川省棠湖中学2020-2021学年高三上学期第一次月考数学(文)试题四川省阆中市东风中学2020-2021学年高三11月月考数学(文)试题甘肃省武威第六中学2021届高三上学期第一次过关考试(开学考试)数学(理)试题
3 . 以平面直角坐标系
的原点
为极点,
轴的正半轴为极轴,取相同的单位长度建立极坐标系,直线
的极坐标方程为
,曲线
的参数方程为
(
为参数).
(Ⅰ)求直线
的直角坐标方程和曲线
的普通方程;
(Ⅱ)求曲线
上的动点到直线
距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.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/cbb6673d1fdeffaa8be277571802a2ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/484f12db4a6a28128467d5445d403d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(Ⅰ)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(Ⅱ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2020-06-16更新
|
393次组卷
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2卷引用:辽宁省大连市2020届高三第二次模拟考试数学文科试题
4 . 在直角坐标系
中,已知点
,
,动点
满足直线
与
的斜率之积为
.记
的轨迹为曲线
.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
.
(1)求
和
的直角坐标方程;
(2)求
上的点到
距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/311497849126f1aaf1da0ec75602eabf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1b47e7bf02b3ca16f7d96b9369e51a3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45ff7e0ef1f622120cc1b18e9d3e80ec.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d50703c46b6153945d718b198f03b4b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e69d2b798744645af88a4fa411344a83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3edbd40e04e2a943051fa83d6e511add.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/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/aa7ee7dce82929e9f332573b6f30e23f.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
名校
5 . 在平面直角坐标系xOy中,以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
;直线l的参数方程为
(t为参数).直线l与曲线C分别交于M,N两点.
(1)写出曲线C的直角坐标方程和直线l的普通方程;
(2)若点P的极坐标为
,
,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c540597109e749508bcb62ef4945c194.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ae7244d6825463be5cd0cbfe476fd04.png)
(1)写出曲线C的直角坐标方程和直线l的普通方程;
(2)若点P的极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d7657720be3edaec2c478bc9899fb236.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fbe706fe88e0a866d03a1c3e2a4d1e83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2020-04-25更新
|
370次组卷
|
3卷引用:2020届辽宁省大连二十四中高三第一次模拟测试数学(理)试题
6 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数,
为常数),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
.
(1)当直线
与曲线
相切时,求出常数
的值;
(2)当
为曲线
上的点,求出
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93cbbc093008169d918b5a6bd9212599.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.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/f04f821f258c7aee82b9cd047546e36b.png)
(1)当直线
![](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)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0203b006524305c3d8ee0b6c34cd872b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc6f3c30a6691c86db14441bd51d777d.png)
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2020-04-07更新
|
396次组卷
|
2卷引用:2020届辽宁省大连一中高三3月模拟测试理科数学试题
7 . 在平面直角坐标系中,以坐标原点O为极点,x轴正半轴为极轴,建立极坐标系,已知曲线C的极坐标方程为:
,经过点
,倾斜角为
的直线l与曲线C交于A,B两点
(I)求曲线C的直角坐标方程和直线l的参数方程;
(Ⅱ)求
的值。
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00999b9a5320bad39b04ad762aa71a0a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/92a0d4c22734cac795de1e5c5fbefa87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(I)求曲线C的直角坐标方程和直线l的参数方程;
(Ⅱ)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba84943545af83f2958b851099c7fd63.png)
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2020-01-29更新
|
443次组卷
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3卷引用:2020届辽宁省大连市高三双基测试数学(文)试题
名校
8 . 极坐标系中椭圆C的方程为
,以极点为原点,极轴为
轴非负半轴,建立平面直角坐标系,且两坐标系取相同的单位长度.
(Ⅰ)求该椭圆的直角坐标方程,若椭圆上任一点坐标为
,求
的取值范围;
(Ⅱ)若椭圆的两条弦
,
交于点
,且直线
与
的倾斜角互补,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99fff3d23b6616ce8d2abedb8ea239ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(Ⅰ)求该椭圆的直角坐标方程,若椭圆上任一点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aee82283f06cedef32eb15b87964f5d2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87cb8cde290c8b049d3a634cd394c5ec.png)
(Ⅱ)若椭圆的两条弦
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d78abbad68bbbf12af10cd40ef4c353.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0cc71c2a530b405dfa312a4f1e7e1e6e.png)
您最近一年使用:0次
9 . 以直角坐标系原点O为极点,x轴的正半轴为极轴.已知点P的直角坐标为
,点M的极坐标为
,若直线l过点P,且倾斜角为
,圆C以M点为圆心,4为半径.
求直线l和圆C的极坐标方程;
直线l与x轴y轴分别交于A,B两点,Q为圆C上一动点,求
面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c4c7dfe5610dcea30e49825cfc5f0ae0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c51441cbb6db455a8bf4a9244e7dd03b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01b899be3c4709ec661d84392b167230.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/ebf0eade2bf666f4752f8ccb8d588a7d.png)
您最近一年使用:0次
10 . 在平面直角坐标系
中,直线l的参数方程为
(t为参数,
为直线的倾斜角),以坐标原点为极点,x轴正半轴为极轴建立极坐标系,曲线
和
的极坐标方程分别为
:
,
:
.
(1)求
的直角坐标方程;
(2)若直线l与曲线
,
,分别相交于异于原点的点M,N,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1ff46dabd1f129b7e36d0638fa2c1a05.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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/138e88f582cb647d212db2c797e8ac27.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若直线l与曲线
![](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/084cf5ffced059f5653ee2a1023518b7.png)
您最近一年使用:0次