23-24高二上·上海·课后作业
1 . 在极坐标系中,求曲线
与
的公共点到极点的距离.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/371ed9a8f6647b919b73f4741513e900.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/91f11b5220813e96b65c9af4b5de0f48.png)
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23-24高二上·上海·课后作业
2 . 设质点
为射线
上的动点,已知点
沿着
方向做匀速运动,同时射线
又绕着它的端点
作等角速度旋转,求质点
运动的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a4f605ec0729ce6d72237ad662a06862.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ef4113c492885ba7c47fe42ac792578f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1dde8112e8eb968fd042418dd632759e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ac047e91852b91af639feec23a9598b2.png)
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23-24高二上·上海·课后作业
解题方法
3 . 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
4 . 对于参数方程
,
(1)若r为参数,表示何曲线?
(2)若
为参数且
,表示何曲线?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/53f1230127e4acf941aad86aaa216338.png)
(1)若r为参数,表示何曲线?
(2)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/790fd1b4fe3a98055b08bcb9d332f072.png)
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解题方法
5 . 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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6 . 圆心C的极坐标为
,且圆C经过极点.
(1)求圆C的极坐标方程;
(2)求过圆心C和圆与极轴交点(不是极点)的直线的极坐标方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d6fda16b497a07e8f8db97074ec19b35.png)
(1)求圆C的极坐标方程;
(2)求过圆心C和圆与极轴交点(不是极点)的直线的极坐标方程.
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解题方法
7 . 将下列曲线的参数方程化为普通方程:
(1)
,
;
(2)
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/abc2ce96a9ce127fe496899fa5040bc5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5caabda288fc01cc168938846eec5d2.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/dfd2b15b25c42a9f9a6ba645df6e9232.png)
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解题方法
8 . 在直角坐标系xOy中,曲线
的参数方程为
(t为参数).
(1)当k=1时,
是什么曲线?
(2)当k=2时,
是什么曲线?
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/4ded686cb106366484a63e2c618aff7f.png)
(1)当k=1时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
(2)当k=2时,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
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解题方法
9 . 将下列参数方程化为普通方程,并说明它们各表示什么曲线?
(1)
(t为参数,a、b为正常数);
(2)
,
.
(1)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/323803f0cee710037d49d572a30c855a.png)
(2)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2be8ac39360e82532aa26df730cf9d1f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c414f1528d2592c7b16d68bf8760da15.png)
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解题方法
10 . 在直角坐标系xOy中,曲线
:
(
为参数,
),其中
,在以O为极点,x轴正半轴为极轴的极坐标系中,曲线
:
,
:
.若
、
相交于点A,
、
相交于点B,求
的最大值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/1eb71edf8424b30fd942f5316cdad638.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/36a1b09c653185842513e24ebba60bb3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/823ab696d27d40920c39b8c910789380.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/10adc3992efb2badc23f81d36faa206f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/23f3ffe7abc59e2f65d827c8eab8d36a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/bcdebedd02b4ea57f8562443742086d3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b80024f36b7b8604522ba11a6ca129.png)
![](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/b1241216f3c1cb5e73043dd1037f556d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ab94459e87c666facddbe1a23ae1899d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3f4dfec890cdfdda355e19463f3be813.png)
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