问题 填空题

若圆C1x2+y2+2ax+a2-4=0(a∈R)与圆C2x2+y2-2by+b2-1=0(b∈R)外切,则a+b的最大值为______.

答案

C1x2+y2+2ax+a2-4=0(a∈R)的标准方程为(x+a)2+y2=4;

C2x2+y2-2by+b2-1=0(b∈R)的标准方程为x2+(y-b)2=1

∵两圆外切

∴a2+b2=9

∵a2+b2≥2ab

∴2(a2+b2)≥(a+b)2

∴18≥(a+b)2

∴-3

2
≤a+b≤3
2

∴a+b的最大值为3

2

故答案为:3

2

阅读理解

阅读理解

       It was Mary's birthday. She received a letter from her uncle. "Dear Mary," he wrote in the letter,

"Happy birthday. I'm sending you some chickens. They will arrive tomorrow. I hope you'll like them.

Uncle Toby."

       Mary was very pleased. She liked eating eggs and chicken. "I can keep the chickens for their eggs

or eat them." She thought.

       When the chicken arrived the next day, they were put in a box. Mary was very happy. She took the

box of the truck and began to carry it into her garden, but the box of chickens was so heavy that she

dropped it.

       The box fell on the ground and broke. The chickens all ran out. They ran here and there. Mary spent

hours in trying to find them.

       A few days later her uncle came. He asked, "Did the chickens arrive safely?" "Yes .but I dropped the box. It broke open and the chickens ran everywhere. It took me the whole morning to look for them.

" Mary said.

       "Did you find them all?" asked her uncle. "I hope so," Mary answered, "but I only caught eleven of

them." "That's very interesting. I only sent you six." Her uncle said with a smile.

1. Mary received a letter from her __________.

A. aunt                  

B. uncle                

C. grandfather              

D. friend

2. When she received her present, Mary was _________.

A. happy          

B. sad            

C. worried            

D. unhappy

3. Why did Mary drop the box? Because _________.

A. she didn't like the present            

B. the box was too heavy

C. she wanted to break the box        

D. she couldn't wait to look at her present

4. It took her ________ to find the chickens.

A. an hour        

B. two hours    

C. three hours          

D. the whole morning

5. Did Mary know how many chickens her uncle sent her?

A. Yes, she did    

B. Yes, she didn't  

C. No, she did.          

D. No. she didn't

单项选择题 A1型题