9.(2009北京理)椭圆的焦点为，点在

椭圆上，若，则_________；

的小大为__________.　　　　　　　　　　　　　　

[答案]　　　　　　　　　　　　　　　　　

[解析]本题主要考查椭圆的定义、焦点、长轴、短轴、焦距之间的关系以及余弦定理. 属

于基础知识、基本运算的考查.

　　　　 ∵，

∴，

∴，

又，　　　　　 (第12题解答图)

∴，

又由余弦定理，得，

∴，故应填.

8.(2009北京理)设是偶函数，若曲线在点处的切线的斜率为1，则该曲线在处的切线的斜率为_________.

[答案]

[解析]本题主要考查导数与曲线在某一点处切线的斜率的概念. 属于基础知识、基本运算

的考查.

取，如图，采用数形结合法，

易得该曲线在处的切线的斜率为.

故应填.

(第11题解答图)

7.(2009北京文)椭圆的焦点为，点P在椭圆上，若，则　　　　 ；的大小为　　　　 .

[答案]

.w[解析]本题主要考查椭圆的定义、焦点、长轴、短轴、焦距之间的关系以及余弦定理. 属于基础知识、基本运算的考查.

　　　　 ∵，

∴，

∴，

又，∴，　 (第13题解答图)

又由余弦定理，得，

∴，故应填.

6.(2009重庆卷理)已知双曲线的左、右焦点分别为，若双曲线上存在一点使，则该双曲线的离心率的取值范围是　　　　　 ．

解法1，因为在中，由正弦定理得

则由已知，得，即，且知点P在双曲线的右支上，

设点由焦点半径公式，得则

解得由双曲线的几何性质知，整理得

解得，故椭圆的离心率

解法2 由解析1知由双曲线的定义知　　

，由椭圆的几何性质知所以以下同解析1.

5.(2009重庆卷文)已知椭圆的左、右焦点分别为，若椭圆上存在一点使，则该椭圆的离心率的取值范围为　　　　　 ．

[答案]

.　　 解法1，因为在中，由正弦定理得

则由已知，得，即

设点由焦点半径公式，得则

记得由椭圆的几何性质知，整理得

解得，故椭圆的离心率

解法2 由解析1知由椭圆的定义知　　

，由椭圆的几何性质知所以以下同解析1.

4.(2009全国卷Ⅰ文)若直线被两平行线所截得的线段的长为，则的倾斜角可以是

　　　　 ①　 ②　 ③　 ④　　 ⑤　　

其中正确答案的序号是　　　　　 .(写出所有正确答案的序号)

[解析]本小题考查直线的斜率、直线的倾斜角、两条平行线间的距离，考查数形结合的思想。

解：两平行线间的距离为，由图知直线与的夹角为，的倾斜角为，所以直线的倾斜角等于或。故填写①或⑤

3.(2009四川卷理)若⊙与⊙相交于A、B两点，且两圆在点A处的切线互相垂直，则线段AB的长度是　　　　　 w

[考点定位]本小题考查圆的标准方程、两直线的位置关系等知识，综合题。

解析：由题知，且，又，所以有，∴。

2.(2009湖北卷文)过原点O作圆x²+y^2_－6x－8y+20=0的两条切线，设切点分别为P、Q，则线段PQ的长为　　　　　　 。

[答案]4

[解析]可得圆方程是又由圆的切线性质及在三角形中运用正弦定理得

1. (2009天津卷理)若圆与圆(a>0)的公共弦的长为，

则___________　 　　。

[考点定位]本小题考查圆与圆的位置关系，基础题。

解析：由知的半径为，由图可知解之得

21.It's bad/good for 对...有害处 　eating more fruit is good for health. 　Don't read in bed. It's bad for your eyes. 　22.It's important/impossible/impolite/difficult for sb. to do sth.对于某人来说做...很重要的 　At school, it's very important for every student to keep their own classrooms clean and tidy. 　Although it is raining heavily, it looks that it's impossible for him not to finish the last 200 meters. 　23. It's time for .../to do sth. 对于...来说做...的时间了 　It's time for us to borrow books from the library. 　It's time for Tom to take medicine. 　24. It's two meters(years) long(old)它两米长(两岁大) 　He is two meters tall. 　The river is twenty meters wide. 　25. keep sb. doing sth 让某人一直做某事 　The headmaster kept me waiting for two hours last time. 　Why do you keep laughing all the time? 　26. keep/make sth. +adj. 让...一直保持... 　It's important for us to keep calm in danger. 　The movie was so sad that it made us cry. 　27. like to do /like doing 喜欢做.... 　My younger sister likes singing and dancing very much. 　What kind of books does she like reading in her free time? 　28. make/let sb.(not)do sth. 让某人做/不做某事 　Make him not lend the book to my younger brother, he will break it. 　To learn English well, the teacher always makes us read aloud in the morning. 　29. neither...nor 既不...也不 　We should come to the party just ath the right time, neither too early nor too late. 　It's neither too cold, nor too hot here all the year round. 　30. not... at all 根本不 　Although life is difficult, each of us doesn't want to give up our hope at all. 　Some have several girlfriends and others have none at all! 　31. not only... but also...　 不仅...而且 　Mike not only finished doing his homework but also helped his sister with her English. 　Today some newly-produced mobile phones can be used not only for taking photos but also for downloading songs from the Internet. 　32. not... until 直到...才 　He didin't stop to have a rest until he finished cleaning the old man's room. 　I didn't understand my mother's love to me until I talked with her yesterday. 　33. one ...the other/ some ...others　 一个…另一个；一些…另一些 　These are my two favotite books. One is called The Monky King, the other is called Harry Potter. 　Somepople say the Indian films are booring, but others say they are great. 　34. see/hear sb do(doing)sth 看见某人做了/正在做 　I heard my parents quarreling after supper. 　I heard someone singing in the next room. 　I heard somone knock a the door when I was cooking. 　35. so... that　 如此…以至于 　The noise outside was so big that we couldn't hear waht the teacher said. 　Kate was so angry that she couldn't say a word. 　36.spend...on(in doing)sth　 在…方面花费 　He spent so much time (in) playing computer games that he was not interested in his lessons. 　She spends $100 on clothes every week. 　37. stop/prevent sb. from doing sth. 阻止某人做某事 　Nothing can stop me from going swimming this afternoon. 　For years, Mike has kept studying how to stop middle school students from losing themselves in net games. 　38. stop to do /doing停下来去做某事 　The boss kept the workers working all the time until they finished all the work. 　Tell him not to stop to rest; it's important moment now. 　39. take /bring sth with sb. 随身携带 　Get the luch which you take with yourself ready, it's time for a meal. 　My friend brought many chocolates with him to visit me. 　40.There is something wrong with... 出了问题/毛病 　There si something wrong with my TV, so we can't watch the match. 　There's something wrong with my computer. Can you help me? 　41. too...to　 太…以至于不能… 　Hearing the news of successful launch of Shenzhou-7, many people were too excited to sleep the whole night. 　The box is too heavy for me to move. 　42. used to 过去常常 　She used to spend a lot of time playing computer games. 　Ther used to be a hospital. 　43. What about.../How about...?　 …怎么样呢？ 　How about going out for a walk after supper? 　I 'm too busy to go tho the movies with you today.How about tomorrow?