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9.(2009北京理)橢圓的焦點為，點在

橢圓上，若，則_________；

的小大為__________.　　　　　　　　　　　　　　

[答案]　　　　　　　　　　　　　　　　　

[解析]本題主要考查橢圓的定義、焦點、長軸、短軸、焦距之間的關系以及余弦定理. 屬

于基礎知識、基本運算的考查.

　　　　 ∵，

∴，

∴，

又，　　　　　 (第12題解答圖)

∴，

又由余弦定理，得，

∴，故應填.

8.(2009北京理)設是偶函數，若曲線在點處的切線的斜率為1，則該曲線在處的切線的斜率為_________.

[答案]

[解析]本題主要考查導數與曲線在某一點處切線的斜率的概念. 屬于基礎知識、基本運算

的考查.

取，如圖，采用數形結合法，

易得該曲線在處的切線的斜率為.

故應填.

(第11題解答圖)

7.(2009北京文)橢圓的焦點為，點P在橢圓上，若，則　　　　 ；的大小為　　　　 .

[答案]

.w[解析]本題主要考查橢圓的定義、焦點、長軸、短軸、焦距之間的關系以及余弦定理. 屬于基礎知識、基本運算的考查.

　　　　 ∵，

∴，

∴，

又，∴，　 (第13題解答圖)

又由余弦定理，得，

∴，故應填.

6.(2009重慶卷理)已知雙曲線的左、右焦點分別為，若雙曲線上存在一點使，則該雙曲線的離心率的取值范圍是　　　　　 ．

解法1，因為在中，由正弦定理得

則由已知，得，即，且知點P在雙曲線的右支上，

設點由焦點半徑公式，得則

解得由雙曲線的幾何性質知，整理得

解得，故橢圓的離心率

解法2 由解析1知由雙曲線的定義知　　

，由橢圓的幾何性質知所以以下同解析1.

5.(2009重慶卷文)已知橢圓的左、右焦點分別為，若橢圓上存在一點使，則該橢圓的離心率的取值范圍為　　　　　 ．

[答案]

.　　 解法1，因為在中，由正弦定理得

則由已知，得，即

設點由焦點半徑公式，得則

記得由橢圓的幾何性質知，整理得

解得，故橢圓的離心率

解法2 由解析1知由橢圓的定義知　　

，由橢圓的幾何性質知所以以下同解析1.

4.(2009全國卷Ⅰ文)若直線被兩平行線所截得的線段的長為，則的傾斜角可以是

　　　　 ①　 ②　 ③　 ④　　 ⑤　　

其中正確答案的序號是　　　　　 .(寫出所有正確答案的序號)

[解析]本小題考查直線的斜率、直線的傾斜角、兩條平行線間的距離，考查數形結合的思想。

解：兩平行線間的距離為，由圖知直線與的夾角為，的傾斜角為，所以直線的傾斜角等于或。故填寫①或⑤

3.(2009四川卷理)若⊙與⊙相交于A、B兩點，且兩圓在點A處的切線互相垂直，則線段AB的長度是　　　　　 w

[考點定位]本小題考查圓的標準方程、兩直線的位置關系等知識，綜合題。

解析：由題知，且，又，所以有，∴。

2.(2009湖北卷文)過原點O作圓x²+y^2_－6x－8y+20=0的兩條切線，設切點分別為P、Q，則線段PQ的長為　　　　　　 。

[答案]4

[解析]可得圓方程是又由圓的切線性質及在三角形中運用正弦定理得

1. (2009天津卷理)若圓與圓(a>0)的公共弦的長為，

則___________　 　　。

[考點定位]本小題考查圓與圓的位置關系，基礎題。

解析：由知的半徑為，由圖可知解之得

21.It's bad/good for 對...有害處 　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.對于某人來說做...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. 對于...來說做...的時間了 　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)它兩米長(兩歲大) 　He is two meters tall. 　The river is twenty meters wide. 　25. keep sb. doing sth 讓某人一直做某事 　The headmaster kept me waiting for two hours last time. 　Why do you keep laughing all the time? 　26. keep/make sth. +adj. 讓...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 喜歡做.... 　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. 讓某人做/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...　 不僅...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　 一個…另一個；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 看見某人做了/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…方面花費 　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停下來去做某事 　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. 隨身攜帶 　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... 出了問題/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 過去常常 　She used to spend a lot of time playing computer games. 　Ther used to be a hospital. 　43. What about.../How about...?　 …怎么樣呢？ 　How about going out for a walk after supper? 　I 'm too busy to go tho the movies with you today.How about tomorrow?