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问题 解答题
已知椭圆C的中心在原点，一个焦点为F(0，
2
)，且长轴长与短轴长的比为
2
：1．
（1）求椭圆C的方程；
（2）若椭圆C上在第一象限内的一点P的横坐标为1，过点P作倾斜角互补的两条不同的直线PA，PB分别交椭圆C于另外两点A，B．求证：直线AB的斜率为定值．
答案

（1）由已知可设椭圆C的方程为：

y2
a2
+
x2
b2
=1(a＞b＞0)

依题意：

a
b
=
2
且a2=b2+2解得：a2=4b2=2

故椭圆C的方程为：

y2
4
+
x2
2
=1…（4分）

（2）证明：由（1）知：P（1，

2
）

由已知设PA：y-

2
=k(x-1)，即：y=kx-(k-
2
)

PB：y-

2
=-k(x-1)，即：y=-kx+(k+
2
)…（6分）

由

y=kx-(k-
2
)
2x2+y2=4
得：(k2+2)x2-2k(k-
2
)+k2-2
2
k-2=0

设A（x1，y1）B（x2，y2）则：x1+1=

2k2-2
2
k
k2+2

故：x1=

k2-2
2
k-2
k2+2
同理：x2=
k2+2
2
k-2
k2+2
…（10分）

直线AB的斜率kAB=

y1-y2
x1-x2
=
k(x1+x2)-2k
x1-x2
=
k
2k2-4
k2+2
-2k
-4
2
k
k2+2
=
-8k
-4
2
k
=
2

所以：直线AB的斜率为定值．…（12分）

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Country-dwellers(农村居民) often say the constant noise, heavy traffic and crowds of the city would drive them mad. Well, they might be right, according to the latest research. City residents are more likely to develop mental illnesses than those who live in villages, a study has found.
Researchers from Cardiff university examined the lifestyles of more than 200,000 people in Sweden and found that those who lived in urban areas were more at risk from mental illnesses than people who lived in villages.
The experts don’t know exactly why this is but they suggest that town and city residents are more likely to be ostracized(排挤) by those around them. They are more likely to experience discrimination(歧视) if they do not fit in, which can lead to them feeling anxious and even developing mental illnesses.
Dr Stanley Zammit, who led the research said that people living in towns and cities are more likely to develop other mental illnesses that result in personality changes — a condition known as non-affective psychosis(非情感性精神病).
Earlier this year an official report found that village-dwellers live an average of two years longer than those living in towns and cities. According to figures from the Office of National Statistics in the UK, men who live in villages are likely to live for between 78 and 79 years, while those in towns and cities can expect to survive to an age of 76. Women on average survive to their 81st birthday in towns and cities, but live to between 82 and 83 in villages. The small marked town of Wimborne Minster in rural Dorset was named the healthiest place to live in.
City residents are more likely to develop illnesses ____小题1:____ than those living in villages,
The way researchers do the research
Examine the ways of _____小题2:____ of more than 200,000 people in Sweden
____小题3:_____ of expert
1.Town and city residents are more likely to be ostracized(排挤) by those around them.
2.They are more likely to go_____小题4:_____ discrimination(歧视)____ 小题5:____ they fit in, which can lead to their ____小题6:_____ and even mental illnesses.
Finding of the research
People living in towns and cities are more likely to develop other mental illnesses that _____小题7:____ personality changes — a condition known as non-affective psychosis(非情感性精神病).
____小题8:_____ from the Office of National Statistics in the UK
1.Village-dwellers live an average of two years longer than those living in towns and cities.
2.Men who live in villages are likely to live ____小题9:____ than those in towns and cities。
3.The _____小题10:____ age of Women in towns and cities is 81.
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A.严密观察引流液的颜色和性状

B.准确记录冲洗量和引流量

C.冲洗速度依据引流液的颜色而定

D.引流不畅时应加压冲洗

E.持续膀胱冲洗法只用于膀胱手术后
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