问题 填空题
已知椭圆
x2
25
+
y2
9
上一点P到两焦点距离之积为m,则当m取最大值时,P点坐标______.
答案

设椭圆的左右焦点为F1、F2

根据椭圆的定义,可得|PF1|+|PF2|=2a=10

∵|PF1|•|PF2|≤[

1
2
(|PF1|+|PF2|)]2=25

当且仅当|PF1|=|PF2|=5时,P到两焦点距离之积为m有最大值为25

∴当m取最大值时,P点位于短轴的顶点,其坐标为(0,±4)

故答案为:(0,±4)

阅读理解

Spending two or three hours playing outdoors each day can reduce(减少)a child’s chance of becoming short-sighted(近视),research shows . It challenges the belif that short-sightedness is caused by computer use , watching TV or reading in weak light .

Australian government researchers believe that sunlight is good for people’s eyes . They compared the vision (视力)and habits of 100 seven-year-old children in China and Australia .In all,30% of the Chinese children were short-sighted .This percentage was ten times higher than Australian children.

Both groups spent a similar amount of time reading, watching TV and playing computer games .However , the Australia children spent an average of two hours a day outdoors ,90 minutes more than the Chinese children.

Professor Ian Morgan said ,“Humans are naturally long-sighted ,but when people begin to go to school and spend little or no time outdoors ,the number of short-sighted peoplegets larger. We are also seeing more and more short-sighted children in cities all around the world –and the main reason may be that city children spend less time outdoors .

Daylight can be hundreds of times brighter than indoor light . But why does playing outside prevent us from becoming short-sighted ? Scientists believe that natural light has a special chemical(化学物质)which stops the eyeball from growing out of shape and prevents people from becoming short-sighted .

So go outdoors .It doesn’t matter if that time is spent having a picnic or playing sports .

根据材料内容选择最佳答案,并将其标号填入题前括号内。

小题1:What can reduce a child's chance of becoming short-sighted according to the passage ?

A.Playing computer games.

B.watching TV.

C.Reading books.

D.Spending 2 or 3 hours playing outside every day.小题2:What does the underlined word "percentage" mean?    

A.百分比

B.功率

C.平均分

D.效率小题3:How much time did the Chinese children spend outdoors according to the research?                                   

A.2 hours.

B.90 minutes.

C.1 hour.

D.30 minutes.小题4:What is the fifth paragraph mainly about?

A.Why people become short-sighted.

B.Why natural light has a special chemical.

C. Why playing outside is good for one's eyesight.

D. Why daylight is much brighter than indoor light.小题5:Which of the following is TRUE according to the passage?  

A.People will all become short-sighted after they begin to go to school.

B.Playing outdoors for 2 or 3 hours every day can help protect your eyesight.

C. Children in Australia are more likely to become short-sighted than those in China.

D. lf you spend 2 or 3 hours playing outside each day, you will become short-sighted.

填空题