题干

已知圆F1:(x+1)2+y2=16,定点F2(1,0),A是圆F1上的一动点,线段F2A的垂直平分线交半径F1A于P点.

(Ⅰ)求P点的轨迹C的方程;

(Ⅱ)四边形EFGH的四个顶点都在曲线C上,且对角线EG,FH过原点O,若kEG•kFH=﹣

3
4
,求证:四边形EFGH的面积为定值,并求出此定值.
上一题 下一题 0.0难度 选择题 更新时间:2012-02-17 01:37:24

答案(点此获取答案解析)

(Ⅰ)解:因为P在线段F2A的中垂线上,所以|PF2|=|PA|.

所以|PF2|+|PF1|=|PA|+|PF1|=|AF1|=4>|F1F2|,

所以轨迹C是以F1,F2为焦点的椭圆,且c=1,a=2,所以

同类题1

将一新鲜叶片放在特殊的装置内,给予不同强度的光照(其他条件保持不变),测得氧气释放速率如下表所示:下列对该数据的分析,错误的是(   )
光照强度
0
2
4
6
8
10
12
14
O2释放率(μL/cm2叶面·min)
-0.2
0
0.2
0.4
0.8
1.2
1.2
1.2

同类题5

    Twelve-year-old Leonardo was born in a poor family in Bambamarca in Peru. He knew how to read but he had never seen a book in his life. So he asked the new priest(牧师)in his village to give him one. But there was no electricity. So Leonardo borrowed candles from the church and sat up all night reading it. The next morning, he was at the door of the priest asking for another book to read.

    John Medcalf, the priest,was moved. He also realized that people would love to read if given a chance. But he knew how difficult it was for Leonardo and those in his village to get books. And yet, no one can be taught to read and write without books. To make people in a poor, faraway area grow to love books,they have to be with them. So he thought the only way was to bring books to people.

    But how could this be done? Mobile libraries or car libraries would be too expensive and difficult to continue in the rocky, hilly land of Peru. So what other method could be used?

    Medcalf got a new idea from the barefoot(赤脚)doctors of China. And that was how the barefoot librarians(图书管理员)first appeared in the villages of northern Peru,almost thirty years ago.

    The librarians began by going from village to village, lending books to villagers. They helped start The Rura1 Library Network of Peru.

    At first,they were teachers of the village schools which these faraway libraries belonged to. But the teachers were not very interested in the job because it meant a lot of hard work. So, village elders took on the job themselves.

    Today, there are 600 village libraries across Peru. The barefoot librarians who walk up to 15 hours a day with bags of books are their lifeline.