问题 解答题
双曲线的离心率等于
5
2
,且与椭圆
x2
9
+
y2
4
=1有公共焦点,求此双曲线的方程.
答案

椭圆

x2
9
+
y2
4
=1焦点为F(±
5
,0),根据题意得双曲线的焦点为F(±
5
,0)(3分)

设双曲线的标准方程为

x2
a2
-
y2
b2
=1,且有c=
5
.(6分)

又由e=

c
a
=
5
2
,得a=2,得b2=c2-a2=5-4=1,(10分)

所求双曲线的方程为

x2
4
-y2=1.(12分)

阅读理解

任务型阅读。

     Have you ever dreamt of winning the lottery ( * * )? Most people will dream of fast cars, large houses, and not

having to work anymore after they win the lottery. In real life, however, that's not always what happens.

     Psychologist David Myers, in his book, says, "Winning the lottery doesn't change people's lives as much as

you might think". Most lottery winners often find that they lose their friends. Their friends will often ask them for

money and these "friends" very often get angry if they don't share the money.

     Lottery winners usually spend some of the money on traveling around the world. However, when the early

excitement of traveling has gone, the happiness that the money brings also disappears (消失). In less than a year

after winning, most winners say that they are not happier than before.

     Too much money can make people unhappy. One study shows that more than 30% of lottery winners lost most

of their money in the first five years and then many of them had money problems. Another study shows that a lot

of people were happily married (结婚的) before they won the lottery, but they had problems with their partners

after winning the money.

     So, you see, although most people dream of winning the lottery, the dream can sometimes turn into a nightmare

(噩梦).

根据短文内容,完成下列句子,每空词数不限.

1. People usually dream of not          after they win the lottery.

2. Although lottery winners get a lot of money, most of them may lose         .

3. Most lottery winners feel they are not so          as before in _________ a year after winning.

4. One study shows over 30% of lottery winners lost          of their money in the first          years.

5. Another study shows that          people had problems with their ________ after winning the lottery.

问答题 简答题