名校
1 . 在极坐标系下,曲线E的极坐标方程为:![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad80596b2f95c8d1e06e923e2e622493.png)
(1)以极坐标系的极点为坐标原点,极轴为x轴正半轴建立平面直角坐标系
,求E直角坐标方程,并说明E的轨迹是什么图形;
(2)A,B,C为曲线E上不同的三点,O为极点,
,证明:
为定值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ad80596b2f95c8d1e06e923e2e622493.png)
(1)以极坐标系的极点为坐标原点,极轴为x轴正半轴建立平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(2)A,B,C为曲线E上不同的三点,O为极点,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e8036a881da6a4eef036529028a11d8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a178c441863ca5be9703d5bcfbfa55b.png)
您最近一年使用:0次
2022-11-28更新
|
559次组卷
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3卷引用:专题10-1 极坐标与参数方程题型归类(讲+练)-1
(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1四川省成都市树德中学2022-2023学年高三上学期11月阶段性测试 数学(文)试题 四川省成都市树德中学2022-2023学年高三上学期11月阶段性测试 数学(理)试题
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解题方法
2 . 在平面直角坐标系中,曲线
的参数方程为
(
为参数),以O为极点,x轴的正半轴为极轴建立极坐标系,曲线
是圆心在极轴上且经过极点的圆,射线
与曲线
交于点
.
(1)求曲线
,
的普通方程;
(2)
,
是曲线
上的两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59cf73e1b94eb456fff9af66c235ef06.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/734a6a1d319648bb969845a9159cdba7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3b70e6ffcb9ab181c7308d812e3137d5.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/299e193c0bb7580f2e0a6f122634f098.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59faa64ad3ae063d1e3dc754c1923227.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/18ed9b5847e95c3ca1b76d76f64a7f77.png)
您最近一年使用:0次
2022-11-20更新
|
620次组卷
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4卷引用:专题12-1 参数方程与极坐标归类-1
2022高三·全国·专题练习
3 . 在直角坐标系
中,曲线
的参数方程为
,(其中
为参数),以原点为极点,以
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
,设点
,曲线
交于
,求
的值.
![](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/422f5c9a218e802b441afadabec54a81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6aaecfa11fd7f4d42e2c8b76e274aff4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4e65611df39794fec95423cc1289d91.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21e9feabc99f62ee569b460e61526e2e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9486e4e76ff07c6c47091e0e4b8bcd7d.png)
您最近一年使用:0次
2022高三·全国·专题练习
4 . 求极坐标
的曲线轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/419184d0481fead88c47bc4f3816ef61.png)
您最近一年使用:0次
5 . 在平面直角坐标系
中,直线
的直角坐标方程为
,曲线
的参数方程为
(
为参数),以原点
为极点,
轴正半轴为极轴建立极坐标系.
(1)求直线
、曲线
的极坐标方程;
(2)若射线
:
分别交直线
,曲线C于M、N两点(点N异于原点О),求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/512f4c29ff276b7f35052ad4cc255ab5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/27140ded06b497cfd728931afcd3b0ab.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)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/13dea1bd3d0dd84b8b6f6ff634c5600c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/309be8577ab98f47afdced566fe5679b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5fad3596e977fdf9f139bb3d0c00f078.png)
您最近一年使用:0次
解题方法
6 . 在平面直角坐标系
中,已知曲线
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
的参数为
(
为参数).
(1)求曲线
和直线
的直角坐标方程;
(2)过原点
引一条射线分别交曲线
和直线
于
、
两点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f09b9a2ea4f4dfbe5f81857aa214c7b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c9121cede0ee0562e23b8a26b34616.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/47ffb694021b52653de5141ae27ba6d0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8edfa16cd6adb98872c604f0e413b09a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/08075b3b73dd2609baad69a496fdd9a8.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
(2)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/701f3b0e2bedfe5195443459072d798e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce1132157a33c82610c2d5035493d024.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a159de0b2d9eb1ae0b7e664e64d3c6c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0914b68f106a912420705b2f3928ca42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1da9dcf6c319174c9ea2b1ceaed1649a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd5edf32d6eb1aa719a91ffb02d23ac1.png)
您最近一年使用:0次
2022-10-19更新
|
583次组卷
|
4卷引用:第01讲 极坐标与参数方程(练)
名校
7 . 在平面直角坐标系xOy中,直线l的参数方程为
(t为参数),以坐标原点O为极点,x轴非负半轴为极轴建立极坐标系,曲线C极坐标方程为:
.
(1)求直线l普通方程与曲线C的直角坐标方程;
(2)过点
的直线l与C相交于A,B两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b938ebac74082afff17c235e6d5dd98e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79de7c27544f42a55d586d49c69a83cd.png)
(1)求直线l普通方程与曲线C的直角坐标方程;
(2)过点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/99296bab1b42898e7ca336a822510258.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de13b1ae79166a207c174dab94cdae6e.png)
您最近一年使用:0次
2022-10-12更新
|
708次组卷
|
4卷引用:第36节 参数方程
8 . 在直角坐标系
中,直线
的参数方程为
(
为参数),以
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)求
的极坐标方程和
的直角坐标方程;
(2)若
与
交于
,
两点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5f20e0b7f90d003bbdc84430e920b22f.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/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/48efce18e6aec0cbe9d340dcf5f11ad3.png)
(1)求
![](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/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/c8a99d2c4a23825f62aadcc40822b5eb.png)
您最近一年使用:0次
2022-09-26更新
|
977次组卷
|
7卷引用:专题20坐标系与参数方程
9 . 在平面直角坐标系xOy中,已知直线
的方程为
,曲线C的参数方程为
(
为参数),若以该直角坐标系的原点О为极点,x轴的正半轴为极轴建立极坐标系.
(1)求直线l和曲线C的极坐标方程;
(2)射线
的极坐标方程为
=
,射线
与曲线C交于点M(异于原点),射线
的极坐标方程为
,射线
与直线
交于点N,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d67158a9694092c5c9a781be29953f96.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f3ffbc3cd63ca329700000906bdb9e36.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求直线l和曲线C的极坐标方程;
(2)射线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d88591679796c52024d11c4de641bdb.png)
![](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/dd15ead753cf2927f51d07c7727c6cd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/80db32fac2352412416e2c95d5d8a35c.png)
您最近一年使用:0次
2022-07-15更新
|
937次组卷
|
3卷引用:专题12-1 参数方程与极坐标归类-1
10 . 在直角坐标系xOy中,直线l的参数方程为
(t为参数),以坐标原点为极点,x轴正半轴为极轴建立极坐标系,曲线C的极坐标方程为ρ2+2ρcos θ+4ρsin θ+4=0.
(1)求l的普通方程和C的参数方程;
(2)已知点M是曲线C上任一点,求点M到直线l距离的最大值,并求出此时点M的坐标.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cb738094683a78b460499070ca9ae352.png)
(1)求l的普通方程和C的参数方程;
(2)已知点M是曲线C上任一点,求点M到直线l距离的最大值,并求出此时点M的坐标.
您最近一年使用:0次
2022-07-14更新
|
526次组卷
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3卷引用:专题10-1 极坐标与参数方程题型归类(讲+练)-2