23-24高二上·上海·课后作业
1 . 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
2 . 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
3 . 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
4 . 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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解题方法
5 . 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
6 . 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
7 . 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
8 . 已知曲线
(
为参数)和定点
,
、
为该曲线的左、右焦点.求经过点
且垂直于直线
的直线l的参数方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/9c9b68e1a5281af1769e74a79f6512f8.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c24095e409b025db711f14be783a406c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/29f0c463dcd546b5769ddf67d998dae4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a3fb78c5f885034612c0e030b920143d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f5076289823db419f94e9c0c8f4aafd9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e86dbcf83cd5d3421b3eed7be7dab32d.png)
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9 . 已知直线
的参数方程为
为参数),圆
的参数方程为
(
为参数).
(1)求直线
的普通方程和圆
的普通方程;
(2)若直线
与圆
的相交弦长不小于
,求实数m的取值范围;
(3)若点
的坐标为
,动点
在圆
上,试求线段
的中点
的轨迹方程.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/12b1b5b172ede59f3702dd0a5e9a686f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/049d5edd51cecf3f8343aa6615225535.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/e170f206fdbbd834aad7580c727e2cc6.png)
(1)求直线
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0f85fca60a11e1af2bf50138d0e3fe62.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5db41a1f31d6baee7c69990811edb9f.png)
(2)若直线
![](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/cf298f00799cbf34b4db26f5f63af92f.png)
(3)若点
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fab8a0cc6504aa4c3a38006f5394b4c2.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/bd33764ff4efddfe11a98a609753715c.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/acc290b44635265137fdf13146b6a6d9.png)
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10 . 已知直线
(t是参数,
),曲线
(t是参数).
(1)若l与E有公共点,求直线l的斜率的取值范围;
(2)若l与E有两个公共点,求直线l的斜率的取值范围.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/78fbd460728c5f82f70eb4bf89b7d0e5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/7e36c9c91220b0f2cbd4a48e8fa90e3d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/877953d7b47721437d1e710657bf8b33.png)
(1)若l与E有公共点,求直线l的斜率的取值范围;
(2)若l与E有两个公共点,求直线l的斜率的取值范围.
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