已知与曲线C：x2+y2-2x-2y+1=0相切的直线l分别交x、y轴于A、B两
题型：解答题
问题：
已知与曲线C：x2+y2-2x-2y+1=0相切的直线l分别交x、y轴于A、B两点，O为原点，|OA|=a，|OB|=b（a＞2，b＞2）．
（1）求证：若曲线C与直线l相切，则有（a-2）（b-2）=2；
（2）求线段AB中点的轨迹方程；
（3）求△AOB面积的最小值．
题型：解答题
Most people have jobs. They go to work nearly every day. Some people are lucky. Either they have very interesting jobs or they make a lot of money. Most people are not so lucky. Either their jobs are not very interesting or they don’t make much money.
The most interesting jobs are often the most difficult. People take a long time to learn how to do them. Doctors study for at least six years after finishing school.
Some young people have interesting and high-pay jobs. Many young players do their work successfully. Football and tennis stars are usually under 35 Years old. Older people usually cannot play these sports very well. They cannot move fast enough. Golf, however is a g
ood sport for older people. Many golf players are quite old, but they can play it successfully.
Most people work until they are 60 or 65 years old. Then they retire (退休) and have a lot of free time. Some people never retire though. These people usually have ver
y interesting jobs. Writers, artists, scientists and actors (演员) usually work until they die. Their work is their life.
根据短文内容，完成下列句子，每空一词。
小题1:Some _______ people have interesting or high-pay jobs, but most people don’t have such good luck.
小题2:Some jobs take a long time to learn because they are _______.
小题3:Young players can move very fast, so many of them play these games like football and tennis very _______.
小题4:Golf is a good sport for _______ people.
小题5: Most people keep _______ until the age of 60 or 65. but writers, artists, scientists and actors can work all their lives.