问题 解答题

已知直线l:y=x+m,m∈R,

(Ⅰ)若以点M(2,0)为圆心的圆与直线l相切于点P,且点P在y轴上,求该圆的方程;

(Ⅱ)若直线l关于x轴对称的直线为l′,问直线l′与抛物线C:x2=4y是否相切?说明理由.

答案

解:(Ⅰ)依题意,点P的坐标为(0,m),

因为MP⊥l,所以

解得m=2,即点P的坐标为(0,2),

从而圆的半径

故所求圆的方程为(x-2)2+y2=8。

(Ⅱ)因为直线l的方程为y=x+m,

所以直线l′的方程为y=-x-m,

得x2+4x+4m=0,△=42-4×4m-16(1-m),

(1)当m=1,即Δ=0时,直线l′与抛物线C相切;

(2)当m≠1,即△≠0,直线l′与抛物线C不相切;

综上,当m=1时,直线l′与抛物线C相切;当m≠1时,直线l与抛物线C不相切。

阅读理解

阅读理解。

    Reader's Digest is a monthly  magazine. Before the 1980s, it  belonged to a  privately  held  company,

which was started in 1922 by Lila Bell Wallace and Dewitt Wallace. This magazine is small and easy to

carry, just half the size of most American magazines, which caused a phrase in 2005, "America in your

pocket." It is the best selling magazine in the USA. At present, its  circulation(发行量)   in the USA has 

reached  10 million copies and the number of the readers there is 38 million. Its global circulation outside

the USA has reached 40 million people throughout more than 70 countries in 21 languages.

    This magazine's focus(焦点) is not news but more of cultural views because the editors think people

now can get timely news from somewhere else. They hope this magazine can give readers something that

is about  special  personal  experiences,  something the readers  can share  with their  families. In  different

countries,  this magazine  provides   a  window  to the world  for the  local  readers. Some  parts of   the

 magazine  are about the local customs and interests of the local readers. The  other  parts  give  the  local

readers information from all over the world.

    This magazine actually used to be a family business until the Wallaces died in the 1980s. Because they

had no children, there was no one to take over the company. Sixteen years ago, this company went public and became a public company.

1. How often does Reader's Digest come out in the USA?    

A. Once a year.    

B. Once a month.    

C. Once a week.    

D. Once a day.

2. What's the number of the readers of this magazine all over the world?    

A. 38 million.      

B. 40 million.        

C. 78 million.      

D. 108 million.

3. This magazine's focus includes the following topics except _________.   

A. something about the timely news       B. some special personal experiences

C. some information from all over the world

D. the local customs and interests of the local readers

选择题