23-24高二上·上海·课后作业
解题方法
1 . 设
、
是常数,参数方程
表示的是什么曲线?
![](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/ec5290f9adf5a0299dd6e8d17b6b2b84.png)
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解题方法
2 . 在平面直角坐标系中,如果曲线
上任意一点的坐标
都是某个变量
的函数,
,
,并且对于
的每一允许值,由方程组(*)所确定的点
都在曲线
上,那么方程组(*)就叫做曲线
的参数方程,变量
叫做参变量或参变数,简称参数.例如,单位圆
的一个参数方程可以是
,
.已知
,
.
(1)若
,求
的值;
(2)求
与
的关系式
.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a2e647c14561826ba9e396acc5a3792c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/52ef198be47a97bd779adb3f8b792833.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/aadb0dc16644a44c37d9463b8957faf4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f240cccaf24af8a796abb95cb42be52e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e5b3fed67b296b0a67d49928dae7e4cc.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b02e39caaa7393864f656660d5dce9b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6a778794e844d82eec2efce68b9c5808.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6712b250bc4218db31853e27b2828b35.png)
(1)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9b384412acba251d87902ab928902f16.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d053b14c8588eee2acbbe44fc37a6886.png)
(2)求
![](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/2329774440278b274651ca465704a856.png)
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名校
解题方法
3 . 已知曲线
的参数方程为
(
为参数).
(1)求曲线
的轨迹方程,并判断轨迹的形状;
(2)设
为曲线
上的动点,且有
,求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b4ea6d6fc4eb4be00cf6cede37756c47.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
(1)求曲线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)设
![](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/603ec320c9795dc869fef7820b96de85.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/17c552e9fe07ab239e67c029a3318901.png)
您最近一年使用:0次
2022-11-15更新
|
702次组卷
|
3卷引用:四川省成都市第七中学2022-2023学年高二上学期期中数学理科试题
4 . 如图,在极坐标系Ox中,圆O的半径为2,半径均为1的两个半圆弧
,
所在圆的圆心分别为
,
,M是半圆弧
上的一个动点.
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/9cb4724d-5baf-4ffb-8b27-0fc4e1e40cd9.png?resizew=172)
(1)当
时,求点M的极坐标;
(2)以O为坐标原点,极轴Ox为x轴正半轴,
的方向为y轴正方向建立平面直角坐标系.若点N为线段
的中点,求点N的轨迹方程.
![](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/0ac26826282f5f23f68c0c826e47e6f5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d4de2411cce374e702613ed54156f20a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2022/7/15/9cb4724d-5baf-4ffb-8b27-0fc4e1e40cd9.png?resizew=172)
(1)当
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/25aa330923dd2f15ed76d442119aa92f.png)
(2)以O为坐标原点,极轴Ox为x轴正半轴,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/755330dce1f013846003b1486afe3b27.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8f26eee4bc9133db37211e28cef00662.png)
您最近一年使用:0次
2022-07-12更新
|
984次组卷
|
9卷引用:四川省成都市2023届高三上学期摸底考试文科数学试题
5 . 已知点
、
的极坐标为
、
,直线
经过
、
两点,曲线
的极坐标方程为
,直线
与曲线
相交于
、
两点. 以极点为坐标原点,极轴为
轴的正半轴,建立平面直角坐标系
.
(1)求直线
的极坐标方程和曲线
的参数方程;
(2)求
.
![](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/171532ccbe6889c0532ac7d9fd99ff4a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5517b9a8b9ec47d6ddd48a961a38e8ad.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.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/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3cda90ec15c07139032c7fed43bcc385.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)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/81dea63b8ce3e51adf66cf7b9982a248.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7ee31829d0d4d5f779a957d7df8058ab.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/084cf5ffced059f5653ee2a1023518b7.png)
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2021-12-15更新
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708次组卷
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3卷引用:云南省昆明市2022届高三摸底考试数学(理)试题
解题方法
6 . 曲线C的方程为
,把曲线
上所有点的横坐标变为原来的
,再向上平移1个单位,得到曲线E,
是曲线E上的动点.
(1)求曲线E的方程;
(2)求
的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c82e7d9f4f7ace849e09e9adcb786b7f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f89eef3148f2d4d09379767b4af69132.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8701e0cce437edc830438b4fe6277d89.png)
(1)求曲线E的方程;
(2)求
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d1fc838e1477179b36ca7481ee2cc1e8.png)
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2021-11-27更新
|
422次组卷
|
2卷引用:江西省南昌市八一中学、洪都中学等4校2021-2022学年高二上学期期中联考数学(理)试题
名校
7 . 已知曲线C的极坐标方程为
.
(1)若直线
过原点,且被曲线C截得弦长最短,求此时直线
的标准形式的参数方程;
(2)
是曲线C上的动点,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/6d4ac1231479c8318f24ceb879072e32.png)
(1)若直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d259822ab64b8626f3893b8432673358.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b88584cf1df43e28d03592c7998b1653.png)
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解题方法
8 . 如图所示,已知圆
,过圆内一点
作两条相互垂直的射线与圆
分别交于点Q、S,以
、
为邻边作矩形
,求矩形顶点R的轨迹.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ccf503ae2e1b201b872fef07dd9ff2cd.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d658b3385c5aa6be7e66f636648af14b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7a5f1641947153c80b987320885a2b57.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9d4aca03910382accfe738520daf689c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/134c3d2c318a33a82da4134dd17fa57e.png)
![](https://img.xkw.com/dksih/QBM/2021/9/24/2815035802148864/2815798248685568/STEM/efe13f2b-2250-4164-8780-35897b3e25f4.png?resizew=270)
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真题
解题方法
9 . 在平面直角坐标系内,下列方程表示什么曲线?画出它们的图形.
(1)
;
(2)
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/357a9573b226db94658611f53519941c.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4428b4b3b491af874ed1d198461a352e.png)
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