问题 填空题

已知椭圆x2+2y2-2=0的两焦点为F1和F2,B为短轴的一个端点,则△BF1F2的外接圆的方程是______.

答案

椭圆x2+2y2-2=0化成标准方程得

x2
2
+
y2
1
=1

∴a2=2,b2=1,可得c2=a2-b2=1,b=c=1

所以两焦点为F1(-1,0)和F2(1,0),

∵B为短轴的一个端点,

∴B(0,1)或B(0,-1)

因此△BF1F2的外接圆是以原点为圆心,半径为1的圆,方程为x2+y2=1

故答案为:x2+y2=1

阅读理解

阅读理解。

     Americans love sports-they love to play them, to watch them on televisions, and to talk about them. But this hobby sometimes has serious results-at least to the players. For example, when people play tennis, sometimes they hurt their elbow and in this way they develop "tennis elbow". Also it is easy to hurt knees in

a football game. These injuries happen while the player is having fun, but they still hurt. A few months ago, Kathleen

     Simmons, who loves playing volleyball, hurt her knee in a volleyball game. Her doctor told her that she needed a very difficult operation (手术) or she might not be able to play again,

     She felt very sad and didn't know what to do. Then Simmons learned about "video operation". With the help of this new science in medicine, doctors can now repair many injuries and get people back on the playing field and back to their jobs much faster. Simmons found a hospital that was using this new science and went to see the doctors there. The doctors told her the operation could help. For this operation, her doctor didn't have to open her knee. Instead he put a very small camera lens (镜头) inside her knee. The lens sent back pictures, which appeared on a television screen. As he worked, he could see the inside of her knee

on the TV. With the help of the large pictures on the screen, the doctor knew exactly what to do when he was making the repairs.

     Simmons started walking five days after her operation. " My knee hurt a lot the first few days," she

said.  "But I felt better very quickly. " Now, six months after her operation,

     Simmons can do everything she did before her injury. "It feels like a new knee," she said.  "I can even

play volleyball again. "

根据短文内容,回答下列问题 。

1. Do Americans love sports?

    ___________________________________________

2. What sport is Simmons interested in?

    ___________________________________________

3. What did the doctor put inside Simmons' knee?

    ___________________________________________

4. What problem may people have when they play sports?

    ___________________________________________

5. What's the advantage of the new science?

    ___________________________________________

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