2024·全国·模拟预测
解题方法
1 . 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,直线
的极坐标方程为
,曲线
的极坐标方程为
.
(1)求直线
的直角坐标方程和曲线
的参数方程;
(2)若点
为曲线
上任意一点,点
到直线
的距离为
,求
的取值范围.
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/937aa64bb643a1f7c1cb33a21cc6a3be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4a90a405f68ef9b3cf8ab1efccd4c237.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/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c02bc0c74292b1e8f395f90935d3174.png)
您最近一年使用:0次
2 . 在极坐标系中,曲线
的极坐标方程为
,直线
与曲线
交于
两点,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
,其中
为坐标原点,求
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef5c101def7894a141dc0c2ee5d6913a.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/7789a500686c7a73770404ead6af0590.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/3a563c50a7f6d10fa46339d7107fc85e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fd908ea0fea10e9ae17b63da04845468.png)
您最近一年使用:0次
名校
3 . 在直角坐标系
中,
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,已知直线
的极坐标方程为
,点A的极坐标为
.
(1)写出
的一个参数方程及直线
的直角坐标方程;
(2)设
为
上的动点,点
满足
,记点
的轨迹为曲线
,求曲线
截直线
所得的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f2a03b95dac0a222906677188f9ef1fa.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/899a11e81e738ef061446a47923d4d41.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1d7a999c36de5c9a9ce876a4a56fa34c.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/669e8dfb2b45e6f74d86408343a18fe2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设
![](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/f243b6c13d79517454562e4c1e0ec7fe.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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2023-06-06更新
|
341次组卷
|
3卷引用:专题13 坐标系与参数方程
4 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数),以平面直角坐标系的原点为极点,
轴的非负半轴为极轴建立极坐标系,已知曲线
的极坐标方程是
.
(1)求曲线
的直角坐标方程与参数方程;
(2)设点
为直线
上
个不同的动点,且
,点
为曲线
上的任意一点,求
面积的取值范围.
![](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/5056c52fbaede0d1e038ecdd10b3565d.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e30d8e9a7538edfedcf51eed7e339363.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/05b09e2d46f94b9ca3caf3f8283619c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/61128ab996360a038e6e64d82fcba004.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce3d196cfee8345bd28a2f3814b676f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4aa0df7f1e45f9de29e802c7f19a4f64.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c28abb154f41e1ca9816c9c9c2433ca.png)
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5 . 已知曲线
和直线
(
为参数).
(1)求曲线
的参数方程和直线
的普通方程;
(2)过曲线
上任意一点
作与直线
夹角为
的直线,交
于点
,求
的最大值与最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cfb7101fa9146fdec51d44b8bf481dc7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/320a79166d81b03a0d0072232edc7de4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)过曲线
![](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/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6b86c22b670a8e9f3896f9e8883fbbb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d063ec7f9dbeba72fabf4437f9400e07.png)
您最近一年使用:0次
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,半圆
的极坐标方程为
.
(1)求
的参数方程;
(2)已知点
在
上,若
在
处的切线与直线
平行,求点
的极坐标.
![](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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/205955768c9b84b2779fb627571165df.png)
(1)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9dac6f4e950ed97fcfe3635c90d80866.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
您最近一年使用:0次
2023-03-17更新
|
656次组卷
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6卷引用:专题21坐标系与参数方程
(已下线)专题21坐标系与参数方程(已下线)专题20坐标系与参数方程(已下线)模拟检测卷03(理科)(已下线)模拟检测卷03(文科)广西南宁市2023届高三第一次适应性测试(文科)数学试题广西南宁市2023届高三第一次适应性测试(理科)数学试题
名校
7 . 在极坐标系下,点
为曲线
:
在极轴
上方的一点,且
,以极点为原点,极轴为
轴正半轴建立平面直角坐标系
.
(1)求曲线
的参数方程;
(2)以
为直角顶点,
为一条直角边作等腰直角三角形
(
在
的右下方),求点
轨迹的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03eeea60522142234171f2705940581b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9e0cb878349009a779d94b1bc40319bb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5880c3a44e340c0689833ec809429670.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)以
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e2c3d2cba96f6f03520c0b3f6e4da03e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e4819c39c281427826e1b3f7a4c2b720.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
您最近一年使用:0次
2023-05-18更新
|
362次组卷
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5卷引用:考向45坐标系与参数方程(重点)-1
(已下线)考向45坐标系与参数方程(重点)-1(已下线)专题10-1 极坐标与参数方程题型归类(讲+练)-1(已下线)专题21 圆锥曲线中的轨迹方程的求法-1黑龙江省哈尔滨市第九中学校2022届高三下学期第五次模拟考试(理科)数学试题四川省绵阳市绵阳中学2023届高三高考模拟理科数学试题(三)
名校
解题方法
8 . 在直角坐标系中,以原点为极点,
轴的非负半轴为极轴,以相同的长度单位建立极坐标系.已知曲线
的极坐标方程为
,直线
的参数方程为
(
为参数)
(1)求曲线
的参数方程与直线
的普通方程;
(2)设点P为曲线C上的动点,点M和点N为直线
上的点,且
,求
面积的取值范围
![](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/cb7e083c34f1df5889f7e65167f8c464.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81e364be2c7c863937b97a470af80235.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设点P为曲线C上的动点,点M和点N为直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1f9bcaec1fcefc0c16094ebf5be90d7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1ed4c4e8edbd179f3fc38a6653f18c1.png)
您最近一年使用:0次
2022-11-09更新
|
630次组卷
|
5卷引用:第01讲 极坐标与参数方程(练)
名校
9 . 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轴的非负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C的普通方程和直线l的直角坐标方程;
(2)设点M的极坐标为
,直线l与曲线C交于A,B两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9380dca2fd7fb8d20c0f5af481d613c8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/649361e842399b796c4cb0b1fe75e2d9.png)
(1)求曲线C的普通方程和直线l的直角坐标方程;
(2)设点M的极坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07c22b1e5f86598a830d503d0746f81d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5bba91242bb7841a41711f02db45fdc0.png)
您最近一年使用:0次
10 . 在平面直角坐标系中,已知直线l:
.以平面直角坐标系的原点O为极点,x轴的正半轴为极轴,建立极坐标系,圆C的极坐标方程为
.
(1)求直线l的极坐标方程和圆C的一个参数方程;
(2)若直线l与圆C交于A,B两点,且
,求m的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81fdea26a77f22155ee52cec20d58d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2014ec8648e67c513b3900229badec5.png)
(1)求直线l的极坐标方程和圆C的一个参数方程;
(2)若直线l与圆C交于A,B两点,且
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0b004f3c29ca828a163255c25323e7cb.png)
您最近一年使用:0次
2022-05-18更新
|
494次组卷
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8卷引用:专题10-1 极坐标与参数方程题型归类(讲+练)-2