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问题 解答题

已知圆C1：x2+y2-4x+2y=0与圆C2：x2+y2-2y-4=0．

（1）求证两圆相交；

（2）求两圆公共弦所在直线的方程；

（3）求过两圆的交点且圆心在直线2x+4y=1上的圆的方程．

答案

（1）证明：圆C1：x2+y2-4x+2y=0与圆C2：x2+y2-2y-4=0化为标准方程分别为圆C1：（x-1）2+（y+1）2=5与圆C2：x2+（y-1）2=5

∴C1（1，-1）与圆C2（0，1），半径都为

5

∴圆心距为

(1-0)2+(-1-1)2
=
5

∴两圆相交；

（2）将两圆的方程作差即可得出两圆的公共弦所在的直线方程，即

（x2+y2-4x+2y）-（x2+y2-2y-4）=0

即x-y-1=0

（3）由（2）得y=x-1代入圆C1：x2+y2-4x+2y=0，化简可得2x2-4x-1=0

∴x=

2±
6
2

当x=

2+
6
2
时，y=
6
2
；当x=
2-
6
2
时，y=-
6
2

设所求圆的圆心坐标为（a，b），则

(a-
2+
6
2
)2+(b-
6
2
)2=(a-
2-
6
2
)2+(b+
6
2
)2
2a+4b=1

∴

a=
3
2
b=-
1
2

∴r2=(

3
2
-
2+
6
2
)2+(-
1
2
-
6
2
)2=
7
2

∴过两圆的交点且圆心在直线2x+4y=1上的圆的方程为(x-

3
2
)2+(y+
1
2
)2=
7
2

阅读理解

These days, many students like playing 3Dgames. Do you know what 3D games are like? In most 3D games, game players need to control a character (人物). The character can be a robot or a soldier. Game players usually use the mouse to make the character move around in his own world. Game players can find things such as food and weapons to help them go on with the game. The character can go straight, sit down, turn left, turn right or pick up things in the game.

Some 3D games have many levels(等级). The character needs to finish different goals（目标） for each level. Game players can against their computers, and sometimes they can play with other players online（在线）. It’s great fun to play 3D games. But playing 3D games for long is not good for our study.

小题1:In most 3D games, game players need to _______.

A．control a character

B．find a robot

C．act as a soldier

D．control the computer小题2:How do game players make the character move around?

A．By using the keyboard.

B．By using the mouse.

C．By telling the directions

D．By moving the computer.小题3:In the game, the character can _________.

A．go straight and sit down

B．turn left and turn right

C．pick up things

D．All the aboves.小题4:Which of the following is NOT true according to the passage?

A．Some 3D games have many levels.

B．The character needs to finish different goals for each level.

C．Game players can only play against their computers.

D．Game players can go online and play with other players together.
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单项选择题

下列更适合通过自保险或风险保留来解决的是( )。

A．小灾小病所需的医疗费用支出

B．意外伤害的损失

C．汽车被盗的财产损失

D．飞机失事的损失
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