直线x-y-5=0被圆x2+y2-4x+4y+6=0所截得的弦的长为_______爱下问搜题

搜题请搜索小程序“爱下问搜题”

问题填空题

直线x-y-5=0被圆x²+y²-4x+4y+6=0所截得的弦的长为______．

答案

圆x²+y²-4x+4y+6=0化为（x-2）²+（y+2）²=2，所以圆的圆心坐标（2，-2），半径为：

2

，

圆心到直线x-y-5=0的距离为：d=

|2+2-5|

12+(-1)2

=

2

2

．

圆心到直线的距离、圆的半径、半弦长满足勾股定理，即半弦长为：

(

2

)2-(

2

2

)2

=

6

2

．

所以弦长为：

6

．

故答案为：

6

．

完形填空

IQ（intelligence quotient智商）is a score that shows a person’s level of intelligence.
People used to believe that some people are born with a high IQ and some aren’t.
32 , a study by scientist at University College London has challenged（挑战）this idea. According to an article last October on the Journal Nature, scientists are beginning to think that our IQ is not a constant（不变的）score.
The scientists tested 33 healthy young people in 2004 between the ages of 12 and 16. Then they did tests again four years later, when the same people were between 16 and 20.
Scientists found big changes in the IQ scores between 2008 and 2004. Some 33 and some fell 34 as many as 21 points.
To test whether these scores were meaningful, the scientists compared them with results from brain scans（扫描）. They found that the IQ changes matched changes in the structure（结构）of the subjects’ brains. “A change in 20 points is a huge 35 ,” said Professor Cathy Price, who led the research. He said it could mean the difference between an average and a 36 person. The team has not found a clear cause for these changes. However, they say it is 37 that education plays a role in changing IQ.
“Here we have shown that children’s 38 is likely to be still developing, ” says Price. “We have to be careful not to write off 39 performers at an early stage. In fact, their IQ may improve in a few more years. ”

B．intelligence

单项选择题

比重比水小的东西会浮在水面上，比重比水大的物体则会沉入水底。木头与铁块绑在一起后沉到了水底，由此可知（）。

A．木头与铁块的比重都比水大

B．该木头与铁块的平均密度比水大

C．木头的比重比水小

D．铁的比重比水大