1 . 在极坐标系中,
表示的曲线是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4efedcacc7ccad8d01a404a3fcc8b22.png)
A.双曲线 | B.抛物线 | C.椭圆 | D.圆 |
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2 . 选修4-4:坐标系与参数方程
在直角坐标系
中,直线
的方程为
,曲线
的参数方程为
(
是参数,
).以
为极点,
轴的非负半轴为极轴建立极坐标系.
(1)分别写出直线
与曲线
的极坐标方程;
(2)若直线
,直线
与曲线
的交点为
,直线
与
的交点为
,求
.
在直角坐标系
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/45cc81cfaccc00aa4b7139de5a35a102.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10580d92bfcedda8f0d35084db78294f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6d221cb1c3d27e184136b8c1aed88a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)分别写出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bc032e33f9b9b8f63e8cff1e2692e4e1.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/5963abe8f421bd99a2aaa94831a951e9.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/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aaff41080fdea43eea7efedf9ebc1498.png)
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2017-02-19更新
|
1491次组卷
|
3卷引用:辽宁省沈阳市东北育才学校2019-2020学年高三上学期第三次模拟数学(文)试题
名校
3 . 已知极坐标系的极点与直角坐标系的原点重合,极轴与
轴的非负半轴重合.若曲线
的极坐标方程为
,直线
的参数方程为
(t为参数).
(1)求曲线
的直角坐标方程与直线
的普通方程;
(2)设点
,直线
与曲线
交于
两点,求
的值.
![](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/32d968b87535257a0e0d5e50df977c22.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/daf80e594b045ebe6282d8447ba1bd32.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
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9538c1cb084f439f61ca964e24eb0c73.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/e52586ca2a3b783bc8092415e2d4bf6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dab988b99be9394ec144a6e25bed9e41.png)
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2016-12-04更新
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1506次组卷
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5卷引用:【全国百强校】辽宁省沈阳市东北育才学校2019届高三第五次模拟数学(理)试题
4 . 若直线
的参数方程为
(
为参数),则
的斜率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d800547c7a21a09e66da6a205182a0c5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
您最近一年使用:0次
5 . 在平面直角坐标系xOy中,已知曲线C1:
(t为参数),C2:
(m为参数).
(1)将C1,C2的方程化为普通方程,并说明它们分别表示什么曲线;
(2)设曲线C1与C2的交点分别为A,B,O为坐标原点,求△OAB的面积的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d0da1ff7c687f825fd6067fb899c811.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3455fe1b302bdd589aabb5f2fe4f40a3.png)
(1)将C1,C2的方程化为普通方程,并说明它们分别表示什么曲线;
(2)设曲线C1与C2的交点分别为A,B,O为坐标原点,求△OAB的面积的最小值.
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6 . 在平面直角坐标系中,以原点为极点,
轴非负半轴为极轴极坐标,曲线
的方程:
(
为参数),曲线
的方程:
.
(1)求曲线
和曲线
的直角坐标系方程;
(2)从
上任意一点
作曲线
的切线,设切点为
,求切线长
的最小值及此时点
的极坐标.
![](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/07e4ebe960c5f93fa737dd698195b481.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/da60a9866c56bc9214a679edb63d6cee.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)从
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
您最近一年使用:0次
名校
7 . 在平面直角坐标系
中,以坐标原点
为极点,以
轴正半轴为极轴建立极坐标系.已知曲线
的极坐标方程为
,射线
与曲线
交于点
,点
满足
,设倾斜角为
的直线
经过点
.
(1)求曲线
的直角坐标方程及直线
的参数方程;
(2)直线
与曲线
交于
、
两点,当
为何值时,
最大?求出此最大值.
![](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/953ddd09e426038f690a84176364e27d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/65125a43aa50b652de8f5614b81f176a.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/acc290b44635265137fdf13146b6a6d9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/883aed020ac213126323824236d898ec.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/acc290b44635265137fdf13146b6a6d9.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b15427e1e39ca4cbfdd2c87917a46126.png)
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2020-01-10更新
|
397次组卷
|
3卷引用:辽宁省沈阳市实验中学2019-2020学年高三上学期12月月考数学试题
8 . 直线
(
为参数)与椭圆
交于
两点,则
的中点坐标为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cbf67acfe1f5f5f8e3c53ee23914f731.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c46ab26e2d950296e9edb81bb20bdcff.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
A.![]() | B.![]() |
C.![]() | D.![]() |
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9 . 已知曲线
的参数方程
(
为参数),在同一直角坐标系中,将曲线
上的点按坐标变换
得到曲线
.
(1)求曲线
的普通方程;
(2)若点
在曲线
上,已知点
,求直线
倾斜角的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b3c7bbe8f0ea8e85d0c3d7e6e3da8ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d2e5643c2bdc7b11293fb0a2b3fe91ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4c8a9c4957431681ddfc77895a88508.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c850811ba59a05e945a665196539a048.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
您最近一年使用:0次
2019-08-06更新
|
511次组卷
|
2卷引用:辽宁省葫芦岛市普通高中2018-2019学年高二下学期数学(文)试题
10 . 在平面直角坐标系
中,直线
的普通方程是
,曲线
的参数方程是
(
为参数).在以
为极点,
轴的正半轴为极轴建立的极坐标系中,曲线
的极坐标方程是
.
(1)写出
及
的极坐标方程;
(2)已知
,
,
与
交于
两点,
与
交于
两点,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/0ca8526916097cfcca035399c342d990.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fa6a67a9cba0a4acffb9c56a124615b0.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/da49da6ef15f2b17022862a56bf8d44e.png)
(1)写出
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/200f24e682c93e02a87f3f9d57dc5d40.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a3c442579603164f3fc19458677d307.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2ef19f98e86ae7504671413780b3b1a9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6544a7dd562c6cc0c9079d75c1bbfbd2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1b7bd1bf71463fc8c1ab6f6f19a61c8d.png)
您最近一年使用:0次
2019-11-30更新
|
516次组卷
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2卷引用:辽宁省六校协作体2019-2020学年高三上学期期中数学(理)试题