1 . 选修4—4:坐标系与参数方程
在平面直角坐标系
中,圆
的参数方程为
(
为参数),直线
经过点
,倾斜角
.
(1)写出圆
的标准方程和直线
的参数方程;
(2)设直线
与圆
相交于
,
两点,求
的值.
在平面直角坐标系
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/eb32a2d6650c4858bc2aa14b93e7d8b0.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/b6332c17b66d4229ba5a5e523e8043fe.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/68e32327d85e440b894e4edd083337c7.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/b0399e1639fe4ccc9d72fa39ad3e1126.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/d374f2e8d3064312a296f394d81b65d4.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/7261e4c5207640559b381d0d87df9cfe.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/e7217adc03094d809b3575769ede66a7.png)
(1)写出圆
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/b6332c17b66d4229ba5a5e523e8043fe.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/d374f2e8d3064312a296f394d81b65d4.png)
(2)设直线
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/d374f2e8d3064312a296f394d81b65d4.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/b6332c17b66d4229ba5a5e523e8043fe.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/522185dc966a45bf9cacccab2946b4ab.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/0f58341da7904bcd8c8d2a68de5900b8.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572056380186624/1572056385626112/STEM/1f0b0a87476b4308921cf811f635bb87.png)
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2016-12-03更新
|
911次组卷
|
2卷引用:2015届辽宁省沈阳市高中三年级教学质量监测一理科数学试卷
2 . 在直角坐标系
中,以O为极点,x轴正半轴为极轴建立极坐标系,曲线C1的极坐标方程为
,曲线C2的参数方程为
(
为参数,
),则C1与C2有______ 个不同公共点.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/df7f3e1a862e4d85b4d6f99442336ebb.png)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572051425050624/1572051431038976/STEM/7ffbe19d17484482b4b578834ae5cbd2.png?resizew=101)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572051425050624/1572051431038976/STEM/3c6ef38f09d34d8da282229e5633a04f.png?resizew=15)
![](https://img.xkw.com/dksih/QBM/2015/3/31/1572051425050624/1572051431038976/STEM/92a39312783e4df690f6cfe16c83d522.png?resizew=53)
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3 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数).以原点
为极点,
轴正半轴为极轴建立极坐标系.
(1)求曲线
的极坐标方程;
(2)若直线
的极坐标方程为
,求直线
被曲线
所截得的线段长.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/301a0fc5746ae6c503d46ae6089fed38.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0d20a51318965087759c1d5dff8627f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b3d1a34ae2b8c77f8d7e355c6d1d667e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e81574a3738c0a314293ff7c74248971.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
(2)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4b1d51a6e648c0ad298fa0ef316d092b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ca66a268d6f46e0e9d5d9151b785be60.png)
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4 . 选修4-4:坐标系与参数方程
在直角坐标平面内,以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,直线
和曲线
(
为参数).
(1)将
与
的方程化为普通方程;
(2)判定直线l与曲线
是否相交,若相交求出
被
截得的弦长.
在直角坐标平面内,以坐标原点O为极点,x轴的非负半轴为极轴建立极坐标系,直线
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/e55df1c65d1a4a46ba1178cf1104bc64.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/da2e32266881479583d3d2d91c95c43c.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/696a34fc6e90465cb30e52a453335aa3.png)
(1)将
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/395c169e23554c14a4920c207c480094.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/309df7e043d642238804b7ed513b4483.png)
(2)判定直线l与曲线
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/309df7e043d642238804b7ed513b4483.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/395c169e23554c14a4920c207c480094.png)
![](https://img.xkw.com/dksih/QBM/2016/2/24/1572496762454016/1572496768425984/STEM/309df7e043d642238804b7ed513b4483.png)
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解题方法
5 . 若
为椭圆
(
为参数)上的点,则
的取值范围是_______ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b21872d8f6a518e0a2993ccf7a795ed2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8d0d9347d20d05f862b684468347066d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8fd1f0ace9ca0b79929e73af6c201c2e.png)
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6 . 以坐标原点
为极点,
轴正半轴为极轴,建立极坐标系,已知曲线
的极坐标方程为
.
(1)求曲线
的普通方程;
(2)将曲线
的图像向左平移1个单位,再将所得图像上各点的横坐标伸长到原来的2倍,纵坐标不变,得到曲线
的图像,若曲线
与
轴的正半轴及
轴的正半轴分别交于点
,在曲线
上任取一点
,且点
在第一象限,求四边形
面积的最大值.
![](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/9e0cb878349009a779d94b1bc40319bb.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)将曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/01c74a907dda6bb7d9d56d009d9df253.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3557809c066e68395b614535a7675e76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/14e902eb263971b466d0fcd91c56b453.png)
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7 . 已知曲线C1的极坐标方程为
,以极点为原点,极轴为x轴的非负半轴建立平面直角坐标系,曲线C2的参数方程为
,求曲线C1与曲线C2交点的直角坐标
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/67617dc9764b727d45cb7ab369c8ea1d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b11a8c78989fb31733c9f5de34c030d1.png)
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8 . 在直角坐标系xOy中以O为极点,x轴正半轴为极轴建立坐标系.圆C1,直线C2的极坐标方程分别为ρ=4sinθ,ρcos(
)=2
.
(Ⅰ)求C1与C2交点的极坐标;
(Ⅱ)设P为C1的圆心,Q为C1与C2交点连线的中点,已知直线PQ的参数方程为
(t∈R为参数),求a,b的值.
![](https://img.xkw.com/dksih/QBM/2016/3/9/1572528042516480/1572528048635904/STEM/5e81ad819ddc411f81035e9384c6a56c.png)
![](https://img.xkw.com/dksih/QBM/2016/3/9/1572528042516480/1572528048635904/STEM/86ae0b0317d447aa8d3ae8803bc676c9.png)
(Ⅰ)求C1与C2交点的极坐标;
(Ⅱ)设P为C1的圆心,Q为C1与C2交点连线的中点,已知直线PQ的参数方程为
![](https://img.xkw.com/dksih/QBM/2016/3/9/1572528042516480/1572528048635904/STEM/1018a79b1cc744aaa6ea4cf9ebba6598.png)
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9 . 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
,将曲线
:
(
为参数),经过伸缩变换
后得到曲线
.
(1)求曲线
的参数方程;
(2)若点
的曲线
上运动,试求出
到直线
的距离的最小值.
![](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/2d49f619e86d0bd6e4210c004d718c5a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/07a682446175c3ff06919f64a94ac597.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a91a72435f1cebe358ef05499010d43a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
(2)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
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2017-02-16更新
|
2863次组卷
|
6卷引用:2016届湖北武汉华中师大一附等高三上第一次联考理数学卷
10 . 函数
的最大值为________ .
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/44dbca1916a5494270506a95b2e68bec.png)
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