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问题 解答题
已知椭圆C的焦点为F1（-1，0）、F2（1，0），点P(-1，
2
2
)在椭圆上．
（1）求椭圆C的方程；
（2）若抛物线y2=2px（p＞0）与椭圆C相交于点M、N，当△OMN（O是坐标原点）的面积取得最大值时，求p的值．
答案

（1）依题意，设椭圆C的方程为

x2
a2
+
y2
b2
=1，

∵2a=|PF1|+|PF2|=

0+(
2
2
)2
+
22+(
2
2
)2
=2
2
，∴a=
2
，c=1，∴b=
a2-c2
=1，

∴椭圆C的方程为

x2
2
+y2=1．

（2）根据椭圆和抛物线的对称性，设M（x0，y0）、N（x0，-y0）（x0，y0＞0），

△OMN的面积S=

1
2
x0×(2y0)=x0y0，

∵M（x0，y0）在椭圆上，∴

x02
2
+y02=1，

∴1=

x02
2
+y02≥2
x02
2
•y02
=
2
x0y0，等号当且仅当
x0
2
=y0时成立，

解

x02
2
+y02=1
x0
2
=y0
（x0，y0＞0）得
x0=1
y0=
2
2
，M（x0，y0）即M(1，
2
2
)．

∵点M在抛物线y2=2px上，∴(

2
2
)2=2p×1，解得p=
1
4
．

∴p=

1
4
．

阅读理解
阅读短文，在方框中的六个选项中选择五个还原到短文中。

A. making it a bit difficult to tell who was whom
B. sending clothes to the children
C. by taking a competition
D. finding out what our children were doing
E. while I was waiting by the school gate
F. because of the cold weather

     It was so cold yesterday evening outside 1______, like many parents waiting for their sons or daughters,
with a coat under the arm 2______. We loving parents noticed the changes of the weather to come up with
the idea -3______. Did they think it was a duty of the parents or were they grateful for what we did? 
     All the lights in the teaching building were brightly on, and at 8:30 pm, the students in their school sports
suits came out of the gate in twos or threes, 4______. It was not only a competition among the students, but
also among the parents-it seems to me that the parents love their only child as if they loved their pet, and that
they would feel happy or unhappy if the pet, 5______ won a prize or fell behind. The results of their study
for the students are just like the competition for the pets. Oh, poor boys and girls! Poor Dad and Mom!
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单项选择题 案例分析题

60岁女性，右眼胀痛，视物不清。伴右侧头痛、恶心、呕吐1天，检查右眼结膜混合充血，角膜水肿，前房浅，瞳孔直径6mm，对光反应无。眼底窥不入，眼压右45mmHg，左17mmHg，房角右窄Ⅳ，左窄Ⅲ

本病诊断为（）

A.急性胃肠炎

B.急性结膜炎

C.急性虹膜睫状体炎

D.急性角膜炎

E.急性闭角型青光眼
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