12-13高三上·江苏扬州·阶段练习
1 . 已知圆
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,直线
的参数方程是
是参数),若直线
与圆
相切,求实数
的值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.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/6a7ad739677805871014786a394fd229.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/294f5ba74cdf695fc9a8a8e52f421328.png)
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(已下线)2012届江苏省扬州中学高三12月练习数学试卷(已下线)2012届江苏省扬州市宝应县高三下学期期初测试数学试卷(已下线)2011-2012学年江苏南京学大教育专修学校高三五月数学试卷【市级联考】江苏省苏州市2019届高三上学期期末学业质量阳光指标调研数学试题江苏省南京市秦淮区2018-2019学年高三下学期第三次模拟考试数学试题
真题
2 . 在平面直角坐标系
中,求过椭圆
(
为参数)的右焦点且与直线
(
为参数)平行的直线的普通方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3516a2cb37f09735c50bf43bc5eaeb19.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cada4595e617c68c84c8081c2f70dcb.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7c3a8d88ebc84c11c4f604dfe2300983.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
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2016-11-30更新
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4卷引用:2011年江苏省普通高中招生考试数学
2011年江苏省普通高中招生考试数学苏教版高中数学 高三二轮 专题25 矩阵与变换坐标系与参数方程 测试专题11.6 参数方程与极坐标(练)-江苏版《2020年高考一轮复习讲练测》(已下线)2012-2013学年甘肃省秦安二中高二下学期期末考试文科数学试卷
10-11高二下·江苏南通·期中
解题方法
3 . 如图,已知点
,
,圆
是以
为直径的圆,直线
:
(
为参数).
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/e4f2e4db-ac03-48e0-984c-07dbf980ee52.png?resizew=164)
(1)写出圆
的普通方程并选取适当的参数改写为参数方程;
(2)过原点
作直线
的垂线,垂足为
,若动点
满足
,当
变化时,求点
的轨迹的参数方程,并指出它是什么曲线.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/351544940f27248ab0796215eef9295a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/161feb34cfc427420ac9571dc15f7668.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/74ea557767b3912fa25882d9201ef7dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/12/26/e4f2e4db-ac03-48e0-984c-07dbf980ee52.png?resizew=164)
(1)写出圆
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)过原点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73465a1f9aa03481295bf6bd3c6903ac.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94a43e654412783a99ac692ca289bc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6581916f5a65edfea257c804efee007e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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10-11高二下·江苏南通·期中
名校
4 . (极坐标与参数方程选讲选做题)设曲线
的参数方程为
(
为参数),直线
的方程为
,则曲线
上到直线
距离为
的点的个数有_个
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb65e8cb1a736c353c3629ce59c96ee1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/26ab55147ca5c0f958af43b0637ee31b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ba7cbd9c973d549145b0c64f21e24e9c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eed5ac4a8424e1ab70633d4c21d90501.png)
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2011·江苏南京·二模
5 . 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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9-10高二下·江苏盐城·期末
6 . 直线
(
为参数,
为常数且
)被以原点为极点,
轴的正半轴为极轴,方程为
的曲线所截,求截得的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d9b8e0c96bcb65ac504ffd7897e7539.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/94440d3e4c073f94f2b266ff99d50e74.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a95311be72fa231af97e4ce0c683d346.png)
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9-10高二下·江苏盐城·期末
7 . 椭圆的参数方程是
(
为参数),则它的离心率为_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b547839ca0518a97ac934bd849a3600.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
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2010·江苏·一模
8 . 已知曲线
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,直线
的参数方程是:
为参数
,求直线
与曲线
相交所成的弦的弦长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/925b34a1e7a48f450d883f9a0197e5c9.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/bba6da52b2adcc0c93d3c39656a14bab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/04582116cd765fcc5a52f44279ad6c94.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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5卷引用:江苏省2010年高考预测试题数学
(已下线)江苏省2010年高考预测试题数学(已下线)2012届江西师大附中高三5月模拟考试理科数学试卷2016届宁夏吴忠中学高三上第四次月考文科数学试卷2016届宁夏吴忠中学高三上学期第四次月考文科数学试卷2016届宁夏吴忠中学高三上学期第四次月考理科数学试卷
真题
名校
9 . 以直角坐标系的原点为极点,
轴的正半轴为极轴,并在两种坐标系中取相同的长度单位,已知直线的极坐标方程为
,它与曲线
(
为参数),相交于两点
和
,则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/334781c7fe448516f45ee4da928b9dea.png)
__________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b2aeafbb2f3f83949ccc9b3d25b7e6c4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/010a23e50e07df3002fc679fccd191a6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/334781c7fe448516f45ee4da928b9dea.png)
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5卷引用:江苏省海门中学2010届高二数学(理科)期末模拟试卷
(已下线)江苏省海门中学2010届高二数学(理科)期末模拟试卷2009年普通高等学校招生全国统一考试理科数学(安徽卷)(已下线)2012届广东揭阳一中、潮州金山中学高三第三次模拟考试理科数学试卷【全国百强校】四川省绵阳市南山中学2017-2018学年高二下学期期中考试数学(文)试题(已下线)考向45坐标系与参数方程(重点)-1
真题
10 . 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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