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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

完形填空

A Bird Startled by the Mere Twang of a Bow-String

　　During the Warring States Period ,in the Wei State there lived a famous archer named Geng Lei. One day, Geng Lei and the King of Wei 小题1:________ on a high terrace saw some birds flying past.小题2:_______ this ，Geng Lei said to the King:"I'll shoot a flying bird down for Your Majesty by drawing a bow with no arrow." The King asked, "Is it possible 小题3:_______ one's archery can attain such a level?" A little later, 小题4:______ wild goose was flying from the east. Geng Lei just drew 小题5:________ bow but didn't shoot an arrow. As expected, the wild goose fell to the ground with the twang.

The King asked in surprise, "How can your archery reach such a high level?"

Geng Lei replied ,"This wild goose 小题6:__________."

　　The King got 小题7:_________(much) surprised, asking, "How do you know it, sir?"　

　  Geng Lei explained, "This wild goose flew slowly and cried 小题8:_______. Its flying slowly suggested that it was still aching with the old wound; its crying sadly suggested that it had strayed long from its flock. 小题9:_______ it heard the twang the wild goose had to flutter hard to fly high for its life. So it is evitably fell down with its old wound burst."

This set phrase figuratively denotes those 小题10:________ have suffered disasters and so have a lingering fear when anything happen.
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单项选择题

塑料基托厚度应为

A．0.5mm

B．1mm

C．4mm

D．3mm

E．2mm
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