问题 填空题

无论a取什么实数,方程x2+2y2-ax+ay-a-1=0表示的椭圆都和一条定直线相交,且截得的弦长为定值,则这个定值是______.

答案

∵x2+2y2-ax+ay-a-1=(x2+2y2-1)-a(x-y+1)=0

方程所表示的曲线是椭圆x2+

y2
1
2
=1与直线x-y+1=0

x2+2y2=1
x-y+1=0
可得3x2+4x+1=0

解可得

x1=-1
y1=0
x2=-
1
3
y2=
2
3

弦长为:

(-1+
1
3
)
2
+(0-
2
3
)
2
=
2
2
3

故答案为:

2
2
3

阅读理解

阅读理解。

     It is common and usual to see people freak out when they face challenges in their life. We all

pass in different life problems and challenges. No one is free of life problems. Only a dead man

faces no problem. As long as you are alive, challenges are everywhere.

     How do you face problems and challenges in your life? Problems and challenges are the building

blocks of your personality. They make you who you are. Besides, whether what happened in your

life builds or destructs you depends on how you look at it. If you take your problems as troubles,

they will be troubles and may cause destruction. If you take them as constructive tools, you are going

to be built up on them.

     Problems are everywhere. No one can avoid them. And they are good too. They open up a

different look and opportunity if you are willing to see. When you face troubles, do not frustrate or

freak out. Just cool yourself to think in a different direction. Think in a positive way. Every problem

has its own good as well as bad sides. Focus on the good one. Look at the bright side.

     Besides, there is always a good person, perhaps your mom or dad, or one of your friends, right

beside you who can turn everything into your best if you are willing to turn to them. No matter what

happens, they will be there to help you. Trust them and they will never let you down. All you need

to know is that you are loved wherever you are.

1. What's the meaning of the underlined phrase "freak out" in Paragraph 1?

A. Feel shy.    

B. Stay calm.  

C. Keep up.    

D. Feel upset.

2. In Paragraph 2, the writer implies that ______.

A. problems cause troubles  

B. attitude is everything

C. challenges can be avoided  

D. personalities are built on failures

3. According to the last paragraph, when we're in trouble, we ______.

A. can only depend on our parents      

B. are not alone

C. should only believe ourselves        

D. are not confident

4. What's the writer's purpose to write the passage?

A. To encourage.  

B. To compare.  

C. To prove.

D. To explain

单项选择题