1 . 在直角坐标系
中,直线
的参数方程为
(
为参数).以坐标原点为极点,
轴的正半轴为极轴建立极坐标系,曲线
的极坐标方程为
.
(1)求直线
的普通方程和曲线
的直角坐标方程;
(2)求
的上的动点到
的距离的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7795aec93c2c7ac2fd93e6747ca6516c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3972e460370496578beb9e34743f6b5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/3fa16f5e131886de5cc9efdea7a36379.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2022-11-13更新
|
322次组卷
|
7卷引用:吉林省梅河口市第五中学2020届高三第六次模拟考试数学(理)试题
吉林省梅河口市第五中学2020届高三第六次模拟考试数学(理)试题吉林省通化市梅河口五中2020届高三高考数学(理科)六模试题(已下线)专题22 坐标系与参数方程-2020年高考数学(文)母题题源解密(全国Ⅰ专版)(已下线)专题22 坐标系与参数方程-2020年高考数学(理)母题题源解密(全国Ⅰ专版)陕西省宝鸡市、汉中市部分校2022-2023学年高三上学期11月期中联考理科数学试题陕西省宝鸡中学2022-2023学年高三上学期11月月考理科数学试题陕西省渭南市临渭区2020-2021学年高二下学期期末文科数学试题
名校
解题方法
2 . 直线的参数方程:
(t为参数),则它的倾斜角为( )
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59b7b832c9aa6af6a57d56a25f77d84b.png)
A.![]() | B.![]() | C.![]() | D.![]() |
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3 . 在直角坐标系xOy中,直线l的参数方程为
'其中t为参数,在以原点O为极点,x轴的正半轴为极轴的极坐标系中,曲线C为∶
.
(1)写出直线l的极坐标方程和曲线C的参数方程;
(2)若曲线C上存在到直线1的距离为
的点,求实数a的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/59554ab7c4a0f197521a54dc6e9fb37c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2030daf33fd69a0ef6ab1a2dedcc7a33.png)
(1)写出直线l的极坐标方程和曲线C的参数方程;
(2)若曲线C上存在到直线1的距离为
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/cf298f00799cbf34b4db26f5f63af92f.png)
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4 . 已知极坐标系中,点
,曲线
的极坐标方程为
,以极点为原点,极轴为
轴的正半轴建立平面直角坐标系,直线
的参数方程为
(
为参数).
(1)求直线
的极坐标方程;
(2)把曲线
上各点的横坐标扩大到原来的5倍,纵坐标扩大到原来的6倍,得到曲线
,
为
上的动点,求线段
的中点
到直线
距离的最小值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b5f3c3ebc629593bda5764f57522d706.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/094ab3a9f3a40f6fc88a4184371dc745.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/ad24691ed8019dc601a335c583c728dc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)把曲线
![](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/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/411461db15ee8086332c531e086c40c7.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dad2a36927223bd70f426ba06aea4b45.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
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2020-09-26更新
|
214次组卷
|
2卷引用:宁夏回族自治区银川市第九中学2021届高三年级第二次月考文科数学试题
2020高三·全国·专题练习
5 . 在平面直角坐标系
中,经过伸缩变换
曲线
变为曲线
.以原点
为极点,
轴正半轴为极轴建立极坐标系,
为极角,直线
的极坐标方程为
,其中
为参数,且
.
(1)求曲线
的直角坐标方程和直线
的参数方程;
(2)设直线
与
轴交于点
,与曲线
交于
、
两点,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c2e133ebf27b807b73d35e97c1b4aa9d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8a9b3304aea584cf2f3a69ff866f5347.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/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a71f796366ca31c5be7f14aa68aca77.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0037403cb9b4c441dbbe9e01338de07.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)设直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/063f4f4ce1d9822e9d5144ca0fc83979.png)
您最近一年使用:0次
6 . 在直角坐标系
中,曲线
的参数方程为
,(
为参数).以
为极点,
轴正半轴为极轴建立极坐标系,射线
的极坐标方程为![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
.已知直线
过点
,且
与
垂直.
(1)求直线
的极坐标方程与曲线
的普通方程;
(2)设直线
与曲线
交于
,
两点,求
与
的等比中项.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/88f034601e9930e14835543086410dc8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.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/c34517f479fb08f6096d2fb0362f3ad0.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0bc1f08c7640e62e8717abf4d44a6c83.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9ccd5ff210fa0216cc381c80acf61d11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60d295a4cc3a58f9f38ee98337313c81.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c34517f479fb08f6096d2fb0362f3ad0.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e9b0f5f44abbc6544a2f672b025b013.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设直线
![](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/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/54a5d7d3b6b63fe5c24c3907b7a8eaa3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ffbd97467518d309bffa46df98f3fd4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1c3b1990466dff7ae4aee764ccc2dd6d.png)
您最近一年使用:0次
解题方法
7 . 在平面直角坐标系xOy中,已知曲线
,直线l的参数方程为
(t参数),以原点为极点、x轴的非负半轴为极轴且取相同的单位长度建立极坐标系.
(1)写出曲线C的参数方程及直线l的极坐标方程;
(2)若直线l上的点A、B对应的参数分别为t,
,点Q在曲线C上,求
面积的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/eb4402aeb853b22f20992156957ef0fd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2f07addd7718476056e40f5851ad9d3.png)
(1)写出曲线C的参数方程及直线l的极坐标方程;
(2)若直线l上的点A、B对应的参数分别为t,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8992e4bc1e15cbb12dcb49e401a1c196.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/16e8c7968d57d2a20065a7cb15c9b4eb.png)
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2020高三·全国·专题练习
解题方法
8 . (1)设
=cos θ,θ为参数,求椭圆
+
=1的参数方程.
(2)将下列参数方程化为普通方程.
(i)
(t为参数);
(ii)
(θ为参数).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e9cd9c1ba23a77c2ca6c6e223196882b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b8d3e830c707265edc4ace52a36ea387.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/295384c1f4389cac2adfceb0565d4ca0.png)
(2)将下列参数方程化为普通方程.
(i)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/902ce43e4acd301b7815e2d5d6c1e5c2.png)
(ii)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c01d198ca545c46ad7827bf7ba8f3b08.png)
您最近一年使用:0次
9 . 在平面直角坐标系
中,直线
的参数方程为
(
为参数),曲线
的普通方程为
,直线
与曲线
交于
,
两点.
(1)求曲线
的参数方程,直线
的普通方程;
(2)设点
,求
的值.
![](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/15cb19b4a1ecb068dd5a458d188c17ea.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.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)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/369709b1b652b992026c83d0e0a8a917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/79188647c574441c2414c3781a0ef543.png)
您最近一年使用:0次
2020-12-21更新
|
189次组卷
|
2卷引用:普通高等学校招生国统一考试2020-2021学年高三上学期 数学(文)考向卷(七)
10 . 在平面直角坐标系
中,曲线
的参数方程为
(
为参数),在以原点为极点,
轴正半轴为极轴的极坐标系中,直线
的极坐标方程为
.
(1)求曲线
和直线
的普通方程;
(2)设点
,
和
交于
、
两点,求
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8411b3ef43f62aa0426055462914f917.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.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/77abfe7f2cfdae08a5c6f7bf8b85dfe6.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/20d059a0d71bddb677c603d84fac444b.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/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7f9e8449aad35c5d840a3395ea86df6d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3979f27823cdcba516dfa885d8afe19d.png)
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