问题 填空题

若直线y=kx-2与抛物线y2=8x交于A、B两点,若线段AB的中点的横坐标是2,则|AB|=______.

答案

y2=8x
y=kx-2
,k2x2-(4k+8)x+4=0,

x1+x2=

4k+8
k2
=4得k=-1或2,

当k=-1时,x2-4x+4=0有两个相等的实数根,不合题意,

当k=2时,|AB|=

1+k2
|x1-x2|=
5
(x1+x2)2-4x1x2
=
5
16-4
=2
15

故答案为:2

15

完形填空
完形填空。先通读下面的短文,掌握其大意,然后在每小题所给的A、B、C、D四个选项中,选出可以填入空白处的最佳选项。
    Thousands of years ago, people did not know   1   to make a fire. When it was very   2    at night, they could
not sleep well. Sometimes lightning hit (打,击) a   3    and started a fire. At first people were both surprised
and   4   to see the fire. They were afraid to go up. Later a few   5   men took some of this fire and made a fire
near their homes. They used the fire to keep them warm and to cook food. 
    When they had a fire, they did not let it   6   burning. If it stopped, they could not start it again. Maybe they
had to   7   for a long time, sometimes for   8  . Later they   9   how to make a fire with pieces of wood. 
    Now we have matches, we can put them in our pockets and make a fire when we want to make it. But we
have to be   10   with fire.
( ) 1.A.what    
( ) 2.A.cold    
( ) 3.A.person  
( ) 4.A.glad    
( ) 5.A.very    
( ) 6.A.stop    
( ) 7.A.work    
( ) 8.A.minutes 
( ) 9.A.forgot  
( ) 10.A.angry      
B.how         
B.hot        
B.mountain (山)  
B.afraid       
B.brave         
B.make          
B.play        
B.hours        
B.decided     
B.pleased     
C.when       
C.warm       
C.field    
C.ready    
C.sad      
C.be         
C.wait     
C.days       
C.learned           
C.careful  
D.where         
D.cool          
D.forest (森林)    
D.tired         
D.happy       
D.start         
D.1ive          
D.years       
D.told          
D.busy        
问答题 简答题