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问题 填空题

两圆x2+y2+2ax+2ay+2a2-1=0与x2+y2+2bx+2by-2=0的公共弦长的最大值是______．

答案

圆x2+y2+2ax+2ay+2a2-1=0化成标准形式，得（x+a）2+（y+a）2=1，

∴该圆表示以M（-a，-a）为圆心，半径为1的圆．

同理圆x2+y2+2bx+2by+2b2-2=0表示以N（-b，-b）为圆心，半径为

2
的圆．

∵圆M的半径为1，圆N的半径为

2
，

∴两圆相交于A、B两点，当线段AB恰好为圆M的直径时，公共弦长达到最大值．

即得两圆公共弦长的最大值为2．

故答案为：2

问答题

Anh’s car required repairs to its steering. She took the car to Repair Limited, a local garage, to have the necessary work completed. Immediately after collecting the car, Anh was driving to the airport in order to travel to Paris on business and the steering on the car failed. As a result, Anh damaged a building adjacent to the road. The subsequent discussions with the owner of the building and the police who attended the accident delayed Anh’s onward journey, causing her to miss the flight. Anh had to pay for a new ticket.Required:

(b) Discuss the extent of liability facing Anh, Repair Limited and the engineer who repaired the steering wheel on behalf of Repair Limited. (6 marks)
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单项选择题

甲欠A合伙企业货款1000元，后A合伙企业中合伙人乙因个人急需向甲借款1000元，则( )。

A．甲还清A合伙企业货款1000元后，而乙不能还款，则甲可以自行取得其在合伙企业中的财产份额用于清偿

B．甲还清A合伙企业货款1000元后，而乙不能还款，则甲可以要求以其从合伙企业中分取的收益用于清偿

C．甲还清A合伙企业货款1000元后，而乙不能还款，则甲可以代位行使乙的管理权

D．甲可以向乙要求两者抵销
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