题目

已知抛物线C：y2=2px过点A(1，1) ①.求抛物线C的方程 ②.过点P(3，−1)的直线与抛物线C交于M，N两个不同的点(均与点A不重合)，设直线AM，AN的斜率分别为k1，k2，求证：k1•k2为定值  答案：解：①∵A在抛物线上        ∴1=2p 即p=         ∴抛物线C的方程为 ②令M（x1,y1）,N(x2,y2) MN:m(y+1)=x-3代入可得 ∴y1+y2=m,   y1*y2=-m-3,  x1+x2=m2+2m+6,   x1*x2=(m+3)2 又k1•k2= =为定值请阅读下面短文，根据短文内容，在下面的表格中填入与文章意思最符合的单词，并将答案写在答题卷相应的位置上，每空一词。For years I have noticed that one common characteristic (特征) that successful people have is curiosity (好奇心). Why is curiosity important? Because it provides you with a fresh perspective (视角) and fresh ideas, Curious people can see things that many other people can’t. So how can you develop curiosity? Here are some tips that you can follow.Expect things to be fun.Instead of expecting things to be boring, expect then to be fun. This small change in your thinking can make a big difference. Once you do it, it will be much easier for you to find the fun side of almost everything. And also, more doors of chances will be open for you.Always have questions in your mind.Whenever you deal with a topic, have questions in your mind. Find the answers and ask new questions. Questions keep your mind busy. They can change your learning process from being borng to being interesting.Take on a new challenge.By taking on a new challenge, you will want to prove to yourself (or perhaps to others) that you can make it. One good way to do that is to create a competition with your friends to find out who can do something faster or better.Connect new things with what you’ve already known.Things will be more exciting if you can connect what you’re learning with what you’ve already know. Why? Because that improves your understanding of the world and allows you to see new things that you haven’t noticed before.Add variety (多样性) to your life.Find new possibilities by stepping into new topics. Read books in new fields. Meet people from all walks of life.All the advice above can be summarized (概括) in just one phrase make things fun.How to Develop CuriosityImportanceCuriosity provides you with a new pers peclive anc new ideas.Curious people can often see more things than many other people.Suggestions● If you expect things to be fun, you can find the fun side of almost anything more 【1】● Keep questioning. 【2】 questions make your mind work and make your learning process more interestion.● If you take on new 【3】, such as creating a competition with your friends, you will want to show that you can succeed.● Connect what you are learning with what you’ve already known and you will 【4】 the world better.● Make some change in your life by meeting 【5】 people and experiencing as many new things as possible.ConclusionMake things fun.