题目

已知两条直线l1：ax－by＋4＝0，l2：(a－1)x＋y＋b＝0.求分别满足下列条件的a和b的值． (1)求直线l1过点(－3，－1)，并且直线l1与直线l2垂直； (2)直线l1与l2平行，并且坐标原点到l1，l2的距离相等． 答案：解 (1)∵l1⊥l2， ∴(a－1)a＋(－b)×1＝0. 即a2－a－b＝0.① 又点(－3，－1)在l1上， ∴－3a＋b＋4＝0.② 由①②解得a＝2，b＝2. (2)∵l1∥l2，且l2的斜率为1－a，∴l1的斜率也存在，即b≠0. ∴＝1－a.∴b＝(a≠1)． 故l1、l2的方程分别可以表示为 l1：(a－1)x＋y＋＝0， l2：(a－1)x＋y＋＝0. ∵原点到l1和l2的距离相等． Worldwide, the most people willing to return your mobile phone if you’ve lost it are to be found in Slovenia, and the fewest in Malaysia. This finding is the result of an interesting study in 32 of the world’s largest cities. Altogether, researchers "lost" 960 new mobile phones. They got back 654 of them, or 68 percent. Prague came in at number eight. There, 23 out of 30 people who were willing to return the mobile phone.It wasn’t a traditional study. Two researchers carefully chose different places, such as areas with high crime (犯罪) and busy downtown shopping areas, to "lose" the phones. When one of the researchers dropped a phone, the other would keep watching from a distance. The honest finders tried their best to find the owner with the help of the address book in the phone. They were told why the study was done and asked why they acted the way they did.It was found that the busier the place where the researchers dropped the phone, the greater the chance of it being returned. Another interesting finding was that women were generally more likely than men to return the phone. Researchers also found that most people still have a sense of honesty. "Crime is simply not good behaviour (行为)," said an expert. "People want to trust others, and want to be trusted."1.Who would be most likely to return a phone, according to the study?A. A man who found it in a park.B. A woman who found it in a park.C. A man who found it in a shopping center.D. A woman who found it in a shopping center.2.Which of the following are findings of the study?a. Prague placed number 8 among the 32 cities.b. Men were less likely to return phones than women.c. It was a traditional and interesting study.d. The busier the place, the greater the chance of the phone being returned.A. abcB. bcdC. acdD. abd3.Why did most people return the phones?A. They knew they belonged to the researchers.B. They wanted to be normal people.C. They wanted to be trusted.D. They didn’t want to commit a crime.4.This passage is mainly about ________.A. why most people returned the phonesB. whether people in busier places are more honestC. a study of people’s honestyD. the honesty of people who return phones