问题 解答题

已知双曲线的方程为5x2-4y2=20两个焦点为F1,F2

(1)求此双曲线的焦点坐标和渐近线方程;

(2)若椭圆与此双曲线有共同的焦点,且有一公共点P满足|PF1|•|PF2|=6,求椭圆的方程.

答案

(1)双曲线的方程为5x2-4y2=20可化为

x2
4
-
y2
5
=1,

∴a=2,b=

5

∴c=

a2+b2
=3,

∴双曲线的焦点坐标(±3,0),渐近线方程为y=±

5
2
x;

(2)由题意,设椭圆的方程为

x2
a2
+
y2
b2
=1(a>b>0),则不妨设|PF1|>|PF2|,

∵|PF1|+|PF2|=2a,|PF1|-|PF2|=4,

∴|PF1|=a+2,|PF2|=a-2,

∵|PF1|•|PF2|=6,

∴(a+2)(a-2)=6,

∴a2=10,

∵c=3,

∴b2=1,

∴椭圆的方程为

x2
10
+y2=1.

单项选择题
改错题

第三节短文改错(共l0小题;每小题l.5分,满分l5分)

此题要求改正所给短文中的错误。对标有题号的每一行做出判断:妞无错误,在该

行右边横线上画一个勾(、/);如有错误(每行只有一个错误),则按下列情况改正:

此行多一个词:把多余的词用斜线(\)划掉,在该行右边横线上写出该词,并也用斜线划掉。

此行缺—个词:在缺词处加一个漏字符号(^),在该行右边横线上写出该加的词。

此行错一个词:在错的词下划一横线,在该行右边横线上写出改正后的词。

注意:原行没有错的不要改。

I just come back from Britain last week.I Was         76._______

luckily enough to be one of the students from many          77. ________   

different country to visit the UK from Feb.16 to 28.       78. ___________   

We paid a visit to a good many of places,like London,     79. _________      

0xford or the Lake District.I learned much about British     80. _________     

culture and history in London, where was my favorite.     81._________     

I also liked Oxford, in which I saw much more old buildings.  82. ________            

The Lake District was beautiful,but it was pity that it         83.__________          

rained heavily when we were there.The most excited thing    84._________           

for me in Britain was that I made a lot of friends there.        85. _________