名校
1 . 选修4-4:坐标系与参数方程
已知曲线
的参数方程为
(
为参数),当
时,曲线
上对应的点为
,以原点
为极点,以
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求证:曲线
的极坐标方程为
;
(2)设曲线
与曲线
的公共点为
,求
的值.
已知曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a154e32f014a393b0ffc775c4347bb5b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7aeb9a94e392f6759b18abed89aacc5e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.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/fd77e0dce4379bd609e84767594525d1.png)
(1)求证:曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7db197c616c76143a2e98b78603cbaee.png)
(2)设曲线
![](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/9a41bf38645a6fb5c2a8ca0048e070ec.png)
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2016-12-04更新
|
365次组卷
|
3卷引用:2016届河南省豫北重点中学高三下第二次联考理科数学卷
2 . 选修4-4:坐标系与参数方程
在直角坐标系xoy中,以o为极点,x轴为正半轴建立直角坐标系,曲线M的方程为
.
(1)求曲线的直角坐标方程;
(2)若点
在曲线M上,点
,FP平行于x轴交曲线M于点
,求证:PO//BA.
在直角坐标系xoy中,以o为极点,x轴为正半轴建立直角坐标系,曲线M的方程为
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572976691970048/1572976698327040/STEM/b698acf5e9914e1080101748ef085344.png)
(1)求曲线的直角坐标方程;
(2)若点
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572976691970048/1572976698327040/STEM/38061d405b334f1f85fcd1b3dc7f32ed.png)
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572976691970048/1572976698327040/STEM/f42df11e3f09431f9cb647982ed15058.png)
![](https://img.xkw.com/dksih/QBM/2016/8/16/1572976691970048/1572976698327040/STEM/9b45d35ef7b54306894cad237ff851ae.png)
您最近一年使用:0次
2016-12-04更新
|
252次组卷
|
2卷引用:2016届海南省农垦中学高三第九次月考理科数学试卷
3 . (1)极坐标系中,圆
的极坐标方程为
,
点为圆心,已知
,求
的面积.
(2)已知
均为正数,求证:
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/21a5d6368b9c4e919b50804e31af4792.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0c82fafeb5bb8250ac529b350c8ce057.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dd936a2405709574af0a73543d94ad9c.png)
(2)已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b811258cf334eaace4a08ca8ea58ff5d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d79bf0b534405c1e9f1c18b1a4a63c40.png)
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4 . 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.设点O为坐标原点,直线
(参数t∈R)与曲线C的极坐标方程为ρsin2θ=4cosθ.
(1)求直线l与曲线C的普通方程;
(2)设直线L与曲线C相交于A,B两点,求证:
.
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572593017864192/1572593023934464/STEM/7a1457160db044e584837d045a1a5360.png)
(1)求直线l与曲线C的普通方程;
(2)设直线L与曲线C相交于A,B两点,求证:
![](https://img.xkw.com/dksih/QBM/2016/4/14/1572593017864192/1572593023934464/STEM/0463343e2ead486588850cd3693be51f.png)
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5 . (1)选修4—4:坐标系与参数方程
已知直线
的极坐标方程是
.以极点为平面直角坐标系的原点,极轴为
轴的正半轴,建立平面直角坐标系,曲线
的参数方程是
(
为参数),直线
和曲线
相交于
两点,求线段
的长.
(2)选修4—5:不等式选讲
已知正实数
满足
,求证:
.
已知直线
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/d444888f055848839539d5647cab437a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/ca868a85f6f2477ebc2a76223fc6041b.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/1e370fa8a8ce4d03af5f98a8f334e9c4.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/e0d937d9a162412fbbc28cedeef6dc07.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/9b728f0d1aa94b4badcaa0a7e97a238d.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/50b047412077481db6322c564729b2a2.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/d444888f055848839539d5647cab437a.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/e0d937d9a162412fbbc28cedeef6dc07.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/acf065c1042f41e8a0bd3a4dc277cefe.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/d3644ae7cd1e48afbab8eb15a1c2174f.png)
(2)选修4—5:不等式选讲
已知正实数
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/807eada2388148fb93840ae94c8fad80.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/1a976964c66c4212994283a24c5f0101.png)
![](https://img.xkw.com/dksih/QBM/2016/1/27/1572470454476800/1572470460252160/STEM/6749cd69bc1244888aa8b8b4b2779824.png)
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6 . 选修4-4:极坐标系与参数方程
已知极坐标系与直角坐标系
有相同的长度单位,以原点
为极点,以
正半轴为极轴,已知曲线
的极坐标方程为
,曲线
的参数方程是
(
为参数,
,射线
与曲线
交于极点
外的三点![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/e479df6a627f4212bd620bd540529dc3.png)
(1)求证:
;
(2)当
时,
两点在曲线
上,求
与
的值.
已知极坐标系与直角坐标系
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/37382debf342480f9cdc7ff94b89681b.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/31cbb7d2f8234e58b060e7ecec37b643.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/e3e2e0d689df481ca82ddaedf907d581.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/3257af45dc5b45c899ec051219dcd134.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/7382e8e1ce53408cbde4d8587b52b558.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/17b95595009843a3827cfff03ebed5ad.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/bd870c9661a74af5b4a643e111511350.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/9721d0bdf16647d0acc16d5debc9ee43.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/033449f234484ff299f621781bfbb646.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/06b99d1866ee40d1bc03daa90ad0dd01.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/3257af45dc5b45c899ec051219dcd134.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/31cbb7d2f8234e58b060e7ecec37b643.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/e479df6a627f4212bd620bd540529dc3.png)
(1)求证:
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/6ec77e53dca84834b513660646cded9b.png)
(2)当
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/0f46001316d74e3c8a69ef0ff496b7b6.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/125e0de7b60d4695a0488108a4e31ec2.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/17b95595009843a3827cfff03ebed5ad.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/7a67c5c1690e4ef09024d6da028e1007.png)
![](https://img.xkw.com/dksih/QBM/2015/5/14/1572109337952256/1572109344276480/STEM/88e8f8fe78f7407f9ed861f0722ead96.png)
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13-14高三·新疆乌鲁木齐·阶段练习
7 . 已知曲线C的极坐标方程为
=2,以极点为原点,极轴为x轴的正半轴建立直角坐标系,P是曲线C上的动点,点A(2,0),M是线段AP的中点.
(1)求点M轨迹的直角坐标方程;
(2)求证:点M到点E(
,0)、F(3、0)的距离之比是常数.
![](https://img.xkw.com/dksih/QBM/2014/8/29/1571846410772480/1571846416621568/STEM/3137d81313cf434b8cb6a97b85486825.png)
(1)求点M轨迹的直角坐标方程;
(2)求证:点M到点E(
![](https://img.xkw.com/dksih/QBM/2014/8/29/1571846410772480/1571846416621568/STEM/dc17f8e7a8c942c1abd6188c7f37ffa5.png)
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2011·江苏南京·二模
8 . 在A、B、C、D四小题中只能选做2题,每小题10,共计20分.请在答题卡指定区域作答.解答应写出文字说明、证明过程或演算步骤.
A、选修4-1:几何证明选讲
如图,已知梯形ABCD为圆内接四边形,AD//BC,过C作该圆的切线,交AD的延长线于E,求证:
ABC∽
EDC.
![](https://img.xkw.com/dksih/QBM/2011/3/31/1570095178530816/1570095183478784/STEM/b97e9a1d3c294214b55318910da378b0.png?resizew=290)
B、选修4-2:矩阵与变换
已知
为矩阵
属于λ的一个特征向量,求实数a,λ的值及
.
C、选修4-4:坐标系与参数方程
在平面直角坐标系xOy中,曲线C的参数方程为
(α为参数),曲线D的参数方程为
(t为参数).若曲线C、D有公共点,求实数m的取值范围.
D、选修4-5:不等式选讲
已知a,b都是正实数,且ab=2.求证:(1+2a)(1+b)≥9.
A、选修4-1:几何证明选讲
如图,已知梯形ABCD为圆内接四边形,AD//BC,过C作该圆的切线,交AD的延长线于E,求证:
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ce4cba95fc7d4853a243f8e3fb20ce70.png)
![](https://img.xkw.com/dksih/QBM/2011/3/31/1570095178530816/1570095183478784/STEM/b97e9a1d3c294214b55318910da378b0.png?resizew=290)
B、选修4-2:矩阵与变换
已知
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0baaf6ae4ed0f84f4d71a56dc8637a74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b9192e87c9f38eb0b37f7b0de686a69.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4663e81a296458a7fd6c589271e52fe.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a335fc7c2c46946f0bf908c78bcc46fa.png)
C、选修4-4:坐标系与参数方程
在平面直角坐标系xOy中,曲线C的参数方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abe3b717472fc1a095d495552cc2f5ce.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e8f42f41fb8ca0617e0b3aae5fe1495f.png)
D、选修4-5:不等式选讲
已知a,b都是正实数,且ab=2.求证:(1+2a)(1+b)≥9.
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真题
9 . A.选修4 - 1:几何证明选讲
如图,在四边形ABCD中,△ABC≌△BAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2fb8b93f-94db-4268-8eb7-7406b5fa70c1.png?resizew=150)
求证:AB∥CD.
B.选修4 - 2:矩阵与变换
求矩阵
的逆矩阵.
C.选修4 - 4:坐标系与参数方程
已知曲线C的参数方程为
(
为参数,
),求曲线C的普通方程.
D.选修4 - 5:不等式选讲
设
≥
>0,求证:
≥
.
如图,在四边形ABCD中,△ABC≌△BAD.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/11/4/2fb8b93f-94db-4268-8eb7-7406b5fa70c1.png?resizew=150)
求证:AB∥CD.
B.选修4 - 2:矩阵与变换
求矩阵
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/efa537c9a8b597c99e7fc6165843593b.png)
C.选修4 - 4:坐标系与参数方程
已知曲线C的参数方程为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/624ae69d616d8118c4e196d5658f4e8a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0fff6e7e2b9f2b68b1647f6350b98dc8.png)
D.选修4 - 5:不等式选讲
设
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d318a788e491a9169b56ba90cf4dbe7c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/662c2bb1fdc296fcd2effd0a9b45fe06.png)
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