名校
1 . 已知极坐标系的极点与直角坐标系的原点重合,极轴与直角坐标系的x轴的正半轴重合,直线的参数方程是
(t为参数),曲线C的极坐标方程为
.
(Ⅰ)求曲线C的直角坐标方程;
(Ⅱ)设直线与曲线C相交于M、N两点,求M、N两点间的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b46fc61f0ebb8c12a8df43b361763ff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c5fdc444697708f273bead395a9fac9.png)
(Ⅰ)求曲线C的直角坐标方程;
(Ⅱ)设直线与曲线C相交于M、N两点,求M、N两点间的距离.
![](https://img.xkw.com/dksih/QBM/2018/6/1/1957916105940992/null/STEM/15142239b7fa4289bc31becdb428feda.png?resizew=260)
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2 . 已知曲线
:
,直线
:
(
为参数).
(1)写出曲线
的参数方程,直线
的普通方程;
(2)求曲线
上任一点
到直线
的距离的最大值和最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f64b7ab668d61bcb8ec6d195c672a81e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e5e0ab0e1aed9189de6be95a150c864.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)求曲线
![](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)
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14-15高二上·黑龙江牡丹江·期中
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3 . 已知直线
的参数方程:
(
为参数),曲线
的参数方程:
(
为参数),且直线交曲线
于
,
两点.
(1)将曲线
的参数方程化为普通方程,并求
时,
的长度;
(2)已知点
,求当直线倾斜角
变化时,
的范围.
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/cebe3e0e4e6c43cba679cd379a11b64a.png?resizew=9)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/37b6357b8d6043e32f68f4d652e58853.png)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/44fdb4c1d9e84577bd56e10f0806a03f.png?resizew=9)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dcf6b822c3fa19cd715a9783be97234.png)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/3fc694a87ea84889ba447499be2cf6f4.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
(1)将曲线
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/28a10f00f0a74d66a663804154770873.png?resizew=16)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/5162bd49efdd4255bfe1036229bc5fe7.png?resizew=43)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/070a49e5db284929bd4f6efa7645449a.png?resizew=31)
(2)已知点
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/1b9b47de4fe74f1293616f0273803598.png?resizew=44)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/1fadfdbc1d934aaab1b7ec22364bae0d.png?resizew=13)
![](https://img.xkw.com/dksih/QBM/2018/7/10/1985430294839296/1986211897139200/STEM/32810b87d0b04a359966be8a6a2dbed6.png?resizew=61)
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2018-07-11更新
|
476次组卷
|
5卷引用:广东省深圳市耀华实验学校2017-2018学年高二下学期期末考试数学(文)试题
名校
4 . 在平面直角坐标系
中,曲线
的参数方程是
(
为参数),以射线
为极轴建立极坐标系,直线
的极坐标方程为
.
(1)将曲线
的参数方程化成普通方程,将直线
的极坐标方程化成直角坐标方程;
(2)求直线
与曲线
相交所得的弦
的长.
![](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/484f12db4a6a28128467d5445d403d22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c3e5af20b2f8c1fba4470f9650989e51.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01aa0c30652c66f3ad1ac97323889d6c.png)
(1)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)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/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2018-05-30更新
|
1239次组卷
|
5卷引用:【全国百强校】广东省深圳市高级中学2019届高三12月模拟考试数学(理)试题
【全国百强校】广东省深圳市高级中学2019届高三12月模拟考试数学(理)试题【全国百强校】河南省郑州外国语学校2018届高三第十五次调研考试数学(理)试题(已下线)2017-2018学年度下学期高中期末备考【通用版】高二【精准复习模拟题】A【基础卷01】【理科数学】(教师版)(已下线)2017-2018学年度下学期高中期末备考【通用版】高二【精准复习模拟题】A【基础卷01】【文科数学】(教师版)重庆市永川北山中学校2019届高三上学期期中数学试题
名校
5 . 在平面直角坐标系
中,曲线
过点
,其参数方程为
(
为参数,
),以坐标原点为极点,以
轴正半轴为极轴,建立极坐标系,曲线
的极坐标方程为
.
(1)写出曲线
的普通方程和曲线
的直角坐标方程;
(2)已知曲线
和曲线
交于
两点(
在
之间),且
,求实数
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/594d4b99d4c5c90fc2e8010cc198551d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/704383c9e8fc0f925b1ca70d2d6437b7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e1e69392d21261afd8e5e5f096634669.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/23dd406c6137b3ba77cc5346508eb3a4.png)
(1)写出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知曲线
![](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/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3ab34ce6cee0673ab0d37b660d57bc07.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
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2018-05-10更新
|
743次组卷
|
2卷引用:【全国市级联考】广东省深圳市宝安区宝安中学等2018届高三七校联合体考前冲刺交流考试数学(理)试题
名校
6 . 在直角坐标系
中,曲线
的参数方程为
(
为参数),其中
.以原点为极点,
轴正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求出曲线
的普通方程和曲线
的直角坐标方程;
(2)已知曲线
与
交于
,
两点,记点
,
相应的参数分别为
,
,当
时,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/2e1929da1e95272ae3e6596e1a946dd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2521ce3378c8f5e55af99c35aa9cd421.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/f42fee1c17c3c66d2c38928f5e3948dc.png)
(1)求出曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)已知曲线
![](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/5963abe8f421bd99a2aaa94831a951e9.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/87c7eb49a823f757461cd5260757b088.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cd84a8f95166367063218ee03ffd5a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bd7ce93c4c5a57748ab3da63802d544f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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2018-04-10更新
|
713次组卷
|
2卷引用:广东省深圳市红岭中学2020届高三上学期第二次统一考试数学(理)试题
名校
7 . 选修4—4:极坐标与参数方程
在平面直角坐标系
中,将曲线
(
为参数) 上任意一点
经过伸缩变换
后得到曲线
的图形.以坐标原点
为极点,x轴的非负半轴为极轴,取相同的单位长度建立极坐标系,已知直线
.
(Ⅰ)求曲线
和直线
的普通方程;
(Ⅱ)点P为曲线
上的任意一点,求点P到直线
的距离的最大值及取得最大值时点P的坐标.
在平面直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e96b0dabd12cac642df82d3337a7f4e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e237f2341245e1154db324aef9fb0174.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/4db35e6d74e083e2cf5e33b063650f5c.png)
(Ⅰ)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(Ⅱ)点P为曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
2018-04-08更新
|
1536次组卷
|
5卷引用:【全国校级联考】广东省(宝安中学、 潮阳一中、桂城中学、南海中学、普宁市第二中学、中山中学、仲元中学)2018届高三5月七校高考冲刺交流数学(文)试题
8 . 选修4-4,坐标系与参数方程
已知在平面直角坐标系xOy中,椭圆C的方程为
,以O为极点,x轴的非负半轴为极轴,取相同的长度单位建立极坐标系,直线
的极坐标方程为
.
(1)求直线
的直角坐标方程;
(2)设M(x,y)为椭圆C上任意一点,求|
x+y﹣1|的最大值.
已知在平面直角坐标系xOy中,椭圆C的方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/00f766adae0a31052a8628bb476ae81f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4d03dd85b6b2e5b242b1644d31a92f5b.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设M(x,y)为椭圆C上任意一点,求|
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/38387ba1cadfd3dfc4dea4ca9f613cea.png)
您最近一年使用:0次
2018-03-19更新
|
374次组卷
|
2卷引用:广东省深圳市南山区2018届高三上学期期末教学质量监测数学(理)试题
9 . 在直角坐标系
中,直线
的参数方程为
(
为参数),在以
为极点,
轴的正半轴为极轴的极坐标系中,曲线
的方程为
.
(1)求直线
和曲线
的直角坐标方程;
(2)已知点
,设直线
与曲线
的两个交点为
,
,若
,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/667d2957c48f79bc6fa2e6f0b60b46f2.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/74b9792422827cf6db4fa1ecde3e623f.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)已知点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3956adfdc26f2b7cd0e3df9bbfe23d80.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4fbfe7995d0907f2627be94d1863f8e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
您最近一年使用:0次
名校
10 . 在平面直角坐标系
中,曲线C:
,直线
:
,直线
:
以坐标原点为极点,x轴正半轴为极轴建立极坐标系.
(1)写出曲线C的参数方程以及直线
,
的极坐标方程;
(2)若直线
与曲线C分别交于O、A两点,直线
与曲线C交于O、B两点,求△AOB的面积.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c171c8206321869c402f0caf587b8747.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b386e2c5d9ad7cec404ce5c40dbebe42.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f75508b798b0e011e91b8d427a102ca.png)
(1)写出曲线C的参数方程以及直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f6f17bc385bafb37e8f964e5eb99cd0.png)
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2018-01-18更新
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15卷引用:【校级联考】广东省深圳实验,珠海一中等六校2019届高三第二次联考数学文试题
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