1 . 参数方程是以参变量为中介来表示直线或曲线上点的坐标的方程,是直线或曲线在同一坐标系下的另一种表现形式.很多曲线(如心脏线、螺线、玫瑰线)都可以用参数方程呈现.在平面直角坐标系
中,直线
的参数方程式
(
为参数),其中
,角
为直线
的倾斜角.曲线
的参数方程是
(
为参数).其中
,直线
与曲线
相交于
、
点.
(1)根据以上的参数方程求出直线
的一般式方程和曲线
的标准方程;
(2)设点
,设点
对应的参数为
,试证明:
;
(3)试问是否存在角
,使得对于任意的点
,表达式
均为定值
,若存在,请求出
及值
(结果用
,
表示);若不存在,请说明理由.
![](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/e9b1cf149172b6c4a6526b25aba683be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a1d5e2dfa2d5b134c85995877eff156b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/73dd51ce19cf9b0ebfa8e42190c72bbf.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.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/e77eee60e92c3e08a5877062cd1e925f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a990942b9fa26d28cee8579325da3675.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5a0c4c098615c6bc7e6dcf72e5b5201a.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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
(1)根据以上的参数方程求出直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bb2baf350ed7e3490fd9e7399ce5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d9fd58e71dcae6cafaf9037d20ebd76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/39b1c2f6f5103b4a981e417b620dd239.png)
(3)试问是否存在角
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/93bb2baf350ed7e3490fd9e7399ce5c6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6df16c0ff148acd2c4eac082120e43be.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/291f17141e5dfbb8e129a9e59d23c120.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/294f5ba74cdf695fc9a8a8e52f421328.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0a6936d370d6a238a608ca56f87198de.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2c94bb12cee76221e13f9ef955b0aab1.png)
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名校
解题方法
2 . 在平面直角坐标系中,定义
、
两点间的直角距离为
,如图,
是圆
当
时的一段弧,
是
与
轴的交点,将
依次以原点
为中心逆时针旋转
五次,得到由六段圆弧构成的曲线.则![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49f3cfe85c4ae1d7ecb30075848e87.png)
_______ .若点
为曲线上任一点,则
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5d6f5adf13b4214666292dd64b947741.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/af405a054bfe7fb7ce40e48d816467e1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bea37e25ba5e11e5e2c428996f74e5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/978ce4ca52b9c915574d50d64ce348b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/239ff12eb6cba0100f0dadb847c90ea8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ed41d321f4c0717ac5b443aad942d9a7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2d5bca00fa20e6e80480b9d06d2e52ee.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/de49f3cfe85c4ae1d7ecb30075848e87.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4298f459599feb1a5ed4dce607b8e3d.png)
![](https://img.xkw.com/dksih/QBM/2021/5/8/2716842768228352/2718602291453952/STEM/3903e3564b0e40039bf873d70ad1e715.png?resizew=166)
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2021-05-11更新
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983次组卷
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5卷引用:湖北省武汉市第二中学2021-2022学年高三上学期暑期模拟数学试题
湖北省武汉市第二中学2021-2022学年高三上学期暑期模拟数学试题福建省南平市2021届高三二模数学试题(已下线)专题14 参数方程与极坐标方程-备战2022年高考数学(文)母题题源解密(全国乙卷)(已下线)专题27 直线与圆的综合应用-1北京市大兴区2023-2024学年高二上学期期中检测数学试题
3 . 已知直线
(
为参数),曲线
(
为参数).
(1)设
与
相交于
两点,求
;
(2)若把曲线
上各点的横坐标压缩为原来的
倍,纵坐标压缩为原来的
倍,得到曲线
,设点
是曲线
上的一个动点,求它到直线
的距离的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b13928ee9d539953bce11ebab61fce8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/061d075835527772d795e91e9ddcf379.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)设
![](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/2fb398137779190b35492d9f06d5fbc3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1f1d63294ee7f92dab9eb37aac5fc064.png)
(2)若把曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/860884c0017c8bceb5b0edff796c144f.png)
![](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/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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4 . 已知集合A={(x,y)|(x﹣3﹣4cosq)2+(y﹣5﹣4sinq)2=4,θ∈R},B={(x,y)|3x+4y﹣19=0}.记集合P=A∩B,则集合P所表示的轨迹的长度为
A.8![]() | B.8![]() | C.8![]() | D.8![]() |
您最近一年使用:0次
2020-03-26更新
|
632次组卷
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3卷引用:2020届湖北省部分省级示范性重点中学教科研协作体高三统一联合考试数学(理)试题
2020届湖北省部分省级示范性重点中学教科研协作体高三统一联合考试数学(理)试题江苏省扬州中学2020-2021学年高二上学期开学检测数学试题(已下线)第2章《圆与方程》 培优测试卷(二)-2021-2022学年高二数学同步培优训练系列(苏教版2019选择性必修第一册)
名校
5 . 正方形
中,点
在以
为圆心且与直线
相切的圆上运动,若
(其中
,
),则
的取值范围是______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411b38a18046fea8e9fab1f9f9b80a5f.png)
![](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/d40b319212a7e7528b053e1c7097e966.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5c4ae2789a5e286e2ce63783a7d60165.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df64046e91b047037f19e4032e3b6de3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5cefeddff52b02a43831beeb4bb6faa4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/febf7413b35cf2889fdb57a6b519087c.png)
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2020-03-16更新
|
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4卷引用:2019届湖北省黄冈中学高三三诊理科数学试题
2019届湖北省黄冈中学高三三诊理科数学试题2019届湖北省黄冈中学高三三诊文科数学试题山西省太原市第五十六中学2020-2021学年高一下学期第一次月考数学试题(已下线)三省三校2022届高三下学期第一次模拟数学(理)试题变式题11-15
19-20高三上·上海浦东新·期中
名校
解题方法
6 . 已知实数
满足
,
,则
的最大值是__________ ;
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2b98742125083374e1463de726ca34db.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fb66f4db41478c23128adc14f2796556.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29ebc856291255f2d4a6c20b982a2442.png)
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2020-02-29更新
|
551次组卷
|
4卷引用:2020届湖北省华中科技大学第二附中高三上学期期中数学试题
2020届湖北省华中科技大学第二附中高三上学期期中数学试题(已下线)上海市华东师范大学第二附属中学2020届高三上学期期中数学试题黑龙江省大庆实验中学2019-2020学年高二下学期第五次网上周测数学(理)试题(已下线)第1-2章 直线与圆(附加篇:参数方程)(单元培优)-2021-2022学年高二数学课后培优练(苏教版2019选择性必修第一册)
解题方法
7 . 平面直角坐标系中,点
、
是方程
表示的曲线
上不同两点,且以
为直径的圆过坐标原点
,则
到直线
的距离为( )
![](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/f33031d14b1ce7df1f07e75072840ba0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
A.2 | B.![]() | C.3 | D.![]() |
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8 . 选修4-4:坐标系与参数方程
在平面直角坐标系
中,曲线
:
(
为参数,实数
),曲线
:
(
为参数,实数
).在以
为极点,
轴的正半轴为极轴的极坐标系中,射线
与
交于
两点,与
交于
两点.当
时,
;当
时,
.
(Ⅰ)求
的值;
(Ⅱ)求
的最大值.
在平面直角坐标系
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/07f68f1754664fa9a4617b92d1c65805.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/0adc300b01ff4883baeb3d2403cf29ea.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/d85b86d238f646d38cda69d9304b6c5f.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/6e640b9ef3d54a9492f1969ec3e00328.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/80c4c073d52c4bb99bc59cdbf59bef1e.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/e940aa43932f48dcb62e7c72a0dab977.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/72ec4e791caa429fa73f8929405651fd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/6e640b9ef3d54a9492f1969ec3e00328.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/e70c515347964b78b8f770f68cf09038.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/10f15b61f2db432d8aad62592868a2f9.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/43a9284ead2e4a71bb68c0bc12dacae7.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/11adf95c05a44c2ab189ee462df13a77.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/0adc300b01ff4883baeb3d2403cf29ea.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/9b8a427e718a435ab6d14bdf1bde0bbd.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/e940aa43932f48dcb62e7c72a0dab977.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/0fc4b2de486e4d66aba043ed2a77914c.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/777ec7cf528b4e4ea24a00d79a6b94c9.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/883a72ebb704471b89b67c6daf17583e.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/fafa99b4cb174513824128054324937d.png)
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/ad2ac34750b04349a6bfcfc222dea1a3.png)
(Ⅰ)求
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/d8e98c0f0e604ac7910e3fa5cd5a2a74.png)
(Ⅱ)求
![](https://img.xkw.com/dksih/QBM/2016/3/25/1572555846664192/1572555990556672/STEM/77b6a5cfee71493cbfb9440a5a891a30.png)
您最近一年使用:0次
2016-12-04更新
|
2163次组卷
|
4卷引用:2016届湖北省襄阳五中高三5月高考模拟一文科数学试卷
2010·湖南长沙·一模
9 . 设椭圆
的左、右焦点分别为F1与
F2,直线
过椭圆的一个焦点F2且与椭圆交于P、Q两点,若
的周长为
.
(1)求椭圆C的方程;
(2)设椭圆C经过伸缩变换
变成曲线
,直线
与曲线
相切
且与椭圆C交于不同的两点A、B,若
,求
面积的取值范围.(O为坐标原点)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/18d781d8551743eb85e594ab52c22ca7.png)
F2,直线
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/7c515639ebc0463da322350cec2abbff.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/b33b7697e94a44ecb3d1b2a18535f796.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/c7a38f6d2b434726a9cb97aafdaf6375.png)
(1)求椭圆C的方程;
(2)设椭圆C经过伸缩变换
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/09e7d3d47a3c48fea0da11229ddc0e7d.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/ffccad7eba3845e498402a77d8be747e.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/77ace84b00ad4ac9b8d2a69db2b0521a.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/ffccad7eba3845e498402a77d8be747e.png)
且与椭圆C交于不同的两点A、B,若
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/8838660c4ba34cb5a4cec45453b27c82.png)
![](https://img.xkw.com/dksih/QBM/2011/8/31/1570298163838976/1570298169245696/STEM/e32d9c4167a949778f2b219c01f01f7d.png)
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