问题 解答题

已知P为曲线E上的任意一点,F1(﹣1,0),F2(1,0),且|PF1|+|PF2|=2|F1F2|.

(1)求曲线E的方程;

(2)若点P在第二象限,∠F2F1P=120°,求△F2F1P的面积.

答案

解:(1)∵F1(﹣1,0),F2(1,0),

∴|PF1|+|PF2|=2|F1F2|=4.

因此,曲线E表示以F1、F2为焦点,长轴2a=4的椭圆,c=1,b2=a2﹣c2=3

∴曲线E的方程为

(2)∵△F2F1P中,∠F2F1P=120°,F1F2=2

∴根据余弦定理,得|F1F2|2=|PF1|2+|PF2|2﹣2|PF1||PF2|cos120°=4,

化简得|PF1|2+|PF2|2+|PF1||PF2|=4…①

又∵|PF1|+|PF2|=4,可得|PF1|2+|PF2|2+2|PF1||PF2|=16…②

∴②减①,得|PF1||PF2|=12

根据正弦定理,可得△F2F1P的面积S=|PF1||PF2|sin120°=3

阅读理解

I often hear some students say English is difficult, and it gives them a headache. So they can't learn it well. But English is very easy for me. I'm good at it. I'm very glad to tell you something about how I study English.

First, I think an interest in English is very important. When I was in Grade One, we had a new subject-English. It was fresh for me. I was interested in it, so I worked hard at it. Soon we had an English exam and I got a very good mark. How happy I was! After that, I learned English harder and harder. Our English teacher often teaches us English songs, the songs sound nice. I often think how interesting English is!

Second, I think English is a foreign language. I should learn it well in the following ways: Listen to the teacher carefully, speak bravely, read aloud and have a good vocabulary. Then practice again and again, never be tired. And I also have a good habit: Asking whenever(不论何时)I have a question, I must make it clear by asking our English teacher. How happy I am when I understand!

Besides this, I often read English stories, jokes and easy novels. From these I know English is not only interesting, but also useful. They help me understand a lot of things. So to do more reading is an important way to learn English well.

And I also do some exercises from our class magazines, and I often write English diaries. English has become a close friend of mine.

Now I have learned English for more than two years. I always keep the first position in our school. From these words, I hope every student can learn English well.

小题1:Why do some students often “have a headache”?

A.Because they are easy to catch cold.

B.Because it's often very cold

C.Because they think English is easy.

D.Because they don't think English is easy.小题2:The writer tells us that we should be ________ in English if we want to learn it well.

A.interest

B.interested

C.interesting

D.strict小题3:The sentence “I got a very good mark” means ______.

A.I got a good way.

B.I had a good idea.

C.I did badly in the exam.   

D.I did well in the exam.小题4:The writer thinks English is interesting because________.

A.English is full of stories. 

B.English is full of jokes.

C.his teacher often teaches them nice English songs.

D.of nothing

解答题