题目
题型:不详难度:来源:
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020655-48886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020655-65923.jpg)
(1)求点P的轨迹方程;
(2)已知D为点P的轨迹曲线上第一象限弧上一点,O为原点,A、B分别为点P的轨迹曲线与
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020655-24528.png)
答案
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36543.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-78137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-94468.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-94675.png)
解析
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-48933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-15336.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020655-48886.png)
(2)本小题为研究方便,可以设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-16160.png)
然后再四边形OADB的面积表示成关于
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-34689.png)
解:(1)设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-48933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-15336.png)
则
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020658-10720.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020658-25239.png)
因为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020655-48886.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020658-52884.png)
化简得
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36543.png)
所以点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-48933.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36543.png)
(2)依题意得,
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020658-35054.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020659-37753.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020659-51507.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020659-25995.png)
设
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020657-16160.png)
则四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-78137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020659-42696.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020659-35295.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020700-30497.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020700-11288.png)
又因为
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020700-18145.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020700-22316.png)
所以
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020701-26308.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020701-43278.png)
所以四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-78137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-94468.png)
当四边形
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-78137.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020701-41621.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020701-16709.png)
此时
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-36623.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020656-94675.png)
核心考点
试题【已知圆C方程:(x-1)2 + y 2=9,垂直于x轴的直线L与圆C相切于N点(N在圆心C的右侧),平面上有一动点P,若PQ⊥L,垂足为Q,且;(1)求点P的轨】;主要考察你对曲线与方程的应用等知识点的理解。[详细]
举一反三
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020650-48084.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020651-34287.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020646-44114.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020646-42029.png)
A.![]() | B.![]() | C.![]() | D.![]() |
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-25108.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-96453.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-99687.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-23046.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-90042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-75816.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-41267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-78092.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-40553.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-41267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-90042.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-94352.jpg)
(Ⅰ)建立适当的平面直角坐标系,求曲线
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-41267.png)
(Ⅱ)设过点
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-56402.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020638-41267.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-89798.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-83688.png)
若△
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-78471.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-95955.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020639-34667.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-16912.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-28390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-63530.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-28390.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-17382.png)
(Ⅰ)求
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-17382.png)
(Ⅱ)若
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020627-29414.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020626-17382.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020627-81228.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020627-87658.png)
![](http://img.shitiku.com.cn/uploads/allimg/20191026/20191026020617-95650.png)
A.1+![]() | B.2+![]() |
C.3-![]() | D.3+![]() |
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