椭圆基础训练题 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：易 题目：1．已知椭圆长半轴与短半轴之比是5：3，焦距是8，焦点在x 轴上，则此椭圆的标准方程是（ ） （A ）5x 2＋3y 2＝1（B ）25x 2＋9y 2＝1 （C ）3x 2＋5y 2＝1 （D ）9 x 2＋25y 2 ＝1 答案：B 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：易 题目：2．椭圆5x 2 ＋4 y 2＝1的两条准线间的距离是（ ） （A ）52 （B ）10 （C ）15 （D ）3 50 答案：B 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：易 题目：3．以椭圆短轴为直径的圆经过此椭圆的焦点，则椭圆的离心率是（ ） （A ）21（B ）22（C ）23（D ）3 3 答案：B 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：中等 题目：4．椭圆25x 2＋9y 2＝1上有一点P ，它到右准线的距离是4 9 ，那么P 点到 左准线的距离是（ ）。 （A ）5 9 （B ） 516 （C ）441 （D ）5 41 答案：D 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：易 题目：5．已知椭圆x 2＋2y 2＝m ，则下列与m 无关的是（ ） （A ）焦点坐标 （B ）准线方程 （C ）焦距 （D ）离心率 答案：D 编号： 年级：高二、高三 知识点：圆锥曲线 分知识点：椭圆 题型：选择题 难度：易 题目：6．椭圆mx 2＋y 2＝1的离心率是 2 3 ，则它的长半轴的长是（ ） （A ）1 （B ）1或2 （C ）2 （D ）2 1 或1
Unit 1-4易错单选题期中复习基础练习 ( )1. Mr Lin is one of_______ in our school. A. good teachers B. better teachers C. the best teachers D. the best teacher ( )2. Our hometown is famous_______ tea and rice. A. with B. by C. for D. as ( )3. You'd better try_______ again. A. don't be late B. not to be late C. aren't late D. to not be late ( )4. I think this song is popular _______young people. A. to B. for C. from D. with ( )5. Sorry. Would you please_______ it in English again? A. say B. talk C. speak D. tell ( )6. How did you make him _______? A. stop talking B. to stop talking C. stop to talk D. stopped to talk ( )7. I'm too hungry. How nice the food_______! A. feels B. sounds C. looks D. smells ( )8. Tony is a_______ boy. He always gives his picket money to the children in need. A. funny B. patient C. generous D. hard-working ( )9. Both beef and pork _______ my favourite. A. is B. are C. am D. be ( )10.There is a big cake. ____________ share it. A. May be we can B. We may be C. Maybe we can D. Maybe can we ( )11.What’s your best friend like? ___________ A He’s fine, thank y ou B. He likes watching TV C. He’s a teacher D. He’s helpful and generous ( )12. —Which of the two T-shirt will you take? —I’ll take _________. One is for my brother and the other is for myself. A either B. both C. all D. every ( )13. The English story is very easy for me. There are ________ new words in it. A. a little B. little C. many D. few ( )14. They do eye exercises twice a day, so ________ of them ________ glasses. A. a few; put on B. a few; wear C. few; put on D. few; wear ( )15. Things are ________ on the moon ________ on Earth. A. much lighter; than B. much heavier; than C. as heavy; as D. not so light; as ( )16. I have ________ money than you, but I have ________ friends than you. A. more; more B. less; more C. fewer; more D. more; less
椭圆练习题1 A组基础过关 一、选择题(每小题5分，共25分) 1．(2012·厦门模拟)已知椭圆的长轴长是短轴长的2倍，则椭圆的离心率等于 ( )． A.1 2 B. 2 2 C. 2 D. 3 2 解析由题意得2a＝22b?a＝2b，又a2＝b2＋c2 ?b＝c?a＝2c?e＝ 2 2 . 答案B 2．(2012·长沙调研)中心在原点，焦点在x轴上，若长轴长为18，且两个焦点恰好将长轴三等分，则此椭圆的方程是( )． A.x2 81 ＋ y2 72 ＝1 B. x2 81 ＋ y2 9 ＝1 C. x2 81 ＋ y2 45 ＝1 D.x2 81＋ y2 36 ＝1
解析 依题意知：2a ＝18，∴a ＝9,2c ＝1 3×2a ，∴c ＝3， ∴b 2 ＝a 2 －c 2 ＝81－9＝72，∴椭圆方程为x 2 81 ＋ y 2 72 ＝1. 答案 A 3．(2012·长春模拟)椭圆x 2＋4y 2＝1的离心率为( )． A. 32 B.34 C.22 D.23 解析 先将 x 2＋4y 2＝1 化为标准方程x 21＋y 214 ＝1，则a ＝1，b ＝12，c ＝a 2－b 2＝3 2 . 离心率e ＝c a ＝3 2. 答案 A 4．(2012·佛山月考)设F 1、F 2分别是椭圆x 24＋y 2 ＝1的左、右焦点，P 是第一象 限内该椭圆上的一点，且PF 1⊥PF 2，则点P 的横坐标为( )． A ．1 B.83 C ．2 2 D.26 3 解析 由题意知，点P 即为圆x 2＋y 2＝3与椭圆x 24 ＋y 2＝1在第一象限的交点， 解方程组???? ? x 2＋y 2＝3，x 24＋y 2 ＝1，得点P 的横坐标为 26 3 . 答案 D 5．(2011·惠州模拟)已知椭圆G 的中心在坐标原点，长轴在x 轴上，离心率为 3 2 ，且椭圆G 上一点到其两个焦点的距离之和为12，则椭圆G 的方程为( )．
Unit 4 Don’t eat in class.（讲义）Words and Expressions rule /ru?l/ n. 规则；规章 arrive /?'ra?v/ v.到达 (be) on time 准时 hallway /'h??lwe?/ n. 走廊；过道 hall /h??l/ n. 大厅；礼堂 dining /'da?n??/ hall 餐厅 listen /'l?sn/ v. 听；倾听 listen to…听…… fight /fa?t/ v. & n. 打架；战斗 sorry /'s?ri/ adj. 抱歉的；难过的；惋惜的outside /,a ?t'sa?d/ adv. 在外面adj. 外面的 wear /we? / v. 穿；戴 important /?m'p??(r)tnt/ adj. 重要的 bring /br??/ v. 带来；取来 uniform /'ju?n?f??(r)m/ n. 校服；制服quiet /'kwa ??t/ adj. 安静的 out /a?t/ adv. 外出 go out 外出(娱乐) practice /'pr?kt?s/ v. & n. 练习 dish /d??/ n. 碟；盘 do the dishes 清洗餐具 before /b?'f??(r)/ prep. & conj. 在……以前adv. 以前 make (one’s) bed 铺床 dirty /'d??(r)ti/ adj. 脏的 kitchen /'k?t??n/ n. 厨房
more /m??(r)/ adj. & pron. 更多(的) noisy /'n??zi/ adj. 吵闹的 relax /r?'l?ks/v. 放松；休息 read /ri?d/ v. 读；阅读 terrible /'ter?bl/ adj. 非常讨厌的；可怕的 feel /fi?l/ v. 感受；觉得 strict /str?kt/ adj. 严格的；严厉的 be strict (with sb) (对某人)要求严格 remember /r ?'memb?(r)/ v. 记住；记起 follow /'f?l ??/ v. 遵循；跟随 follow the rules 遵守规则 luck /l?k/ n. 幸运；运气 keep /ki?p/ v. 保持；保留 hair /he?/ /her/ n. 头发；毛发 learn /l??(r)n/ v. 学习；学会 Clark /klɑ?(r)k/ 克拉克(姓；男名) Amy /'e?mi/ 埃米(女名) Molly /'m?li/ 莫莉(女名) New York /,nju?'j??(r)k/ 纽约 Role-play John: Hi, my name’s John. It’s my first day at school. Alice: Hi, John. I’m Alice. This is a great school, but there are a lot of rules. John: Really? What are some of the rules? Alice: Well, don’t be late for class. This is very important. John: OK, so we must be on time. Can we bring music players to school? Alice: No, we can’t. And we al ways have to wear the school uniform. John: I see. Alice: Oh, and we also have to be quiet in the library.
一、选择题（每小题只有一个正确答案，每题6分共36分） 1. 椭圆22 1259 x y +=的焦距为。 （ ） A ． 5 B. 3 C. 4 D 8 2．已知双曲线的离心率为2，焦点是（-4,0），（4,0），则双曲线的方程为 （ ） A ． 221412x y -= B. 221124x y -= C. 221106x y -= D 22 1610x y -= 3．双曲线22 134 x y -=的两条准线间的距离等于 （ ） A C. 185 D 165 4.椭圆22 143 x y +=上一点P 到左焦点的距离为3，则P 到y 轴的距离为 （ ） A ． 1 B. 2 C. 3 D 4 5．双曲线的渐进线方程为230x y ±=，(0,5)F -为双曲线的一个焦点，则双曲线的方程为。 （ ） A ． 22149y x -= B. 22194x y -= C. 2213131100225y x -= D 2213131225100y x -= 6．设12,F F 是双曲线22221x y a b -=的左、右焦点，若双曲线上存在点A ，使1290F AF ? ∠=且 123AF AF =,则双曲线的离心率为 （ ） A ． 2 B. 2 C. 2 7.设斜率为2的直线l 过抛物线y 2 ＝ax (a ≠0)的焦点F ，且和y 轴交于点A ，若△OAF (O 为坐标原点)的面积为4，则抛物线方程为( ) A ．y 2 ＝±4 B ．y 2 ＝±8x C ．y 2 ＝4x D ．y 2 ＝8x 8．已知直线l 1：4x －3y ＋6＝0和直线l 2：x ＝－1，抛物线y 2 ＝4x 上一动点P 到直线 l 1和直线l 2的距离之和的最小值是( ) A ．2 B ．3 9．已知直线l 1：4x －3y ＋6＝0和直线l 2：x ＝－1，抛物线y 2 ＝4x 上一动点P 到直线
初步圆锥曲线 感受：已知圆O 以坐标原点为圆心且过点1,22?? ? ??? ，,M N 为平面上关于原点对称的两点，已知N 的 坐标为0,3? - ?? ,过N 作直线交圆于,A B 两点 (1）求圆O 的方程; （2)求ABM ?面积的取值范围 二. 曲线方程和方程曲线 （1）曲线上点的坐标都是方程的解； （2）方程的解为坐标的点都在曲线上. 三. 轨迹方程 例题:教材P .３7 A 组.T3 T4 Ｂ组 T2 练习 1.设一动点P 到直线:3l x =的距离到它到点()1,0A 的距离之比为3 ,则动点P 的轨迹方程是____ 练习２.已知两定点的坐标分别为()()1,0,2,0A B -,动点满足条件2MBA MAB ∠=∠，则动点M 的轨迹方程为＿＿_____＿＿__ 总结：求点轨迹方程的步骤： (1）建立直角坐标系 （2）设点:将所求点坐标设为(),x y ,同时将其他相关点坐标化(未知的暂用参数表示)
（3）列式:从已知条件中发掘,x y 的关系，列出方程 （４）化简:将方程进行变形化简，并求出,x y 的范围 四. 设直线方程 设直线方程：若直线方程未给出，应先假设． (1)若已知直线过点00(,)x y ,则假设方程为00()y y k x x ； (２）若已知直线恒过y 轴上一点()t ，0,则假设方程为t kx y +=； （３）若仅仅知道是直线，则假设方程为b kx y += 【注】以上三种假设方式都要注意斜率是否存在的讨论； （4）若已知直线恒过x 轴上一点(,0)t ,且水平线不满足条件（斜率为０),可以假设 直线为x my t 。 【反斜截式，1 m k 】不含垂直于y 轴的情况（水平线） 例题:圆C 的方程为：.0222=-+y x (1)若直线过点）（4,0且与圆C 相交于Ａ，B 两点,且2=AB ,求直线方程． (2）若直线过点） （3,1且与圆C 相切,求直线方程. (3)若直线过点） （0,4且与圆C 相切,求直线方程． 附加:4)4(3:22 =-+-y x C ）（ ． 若直线过点）（0,1且与圆C 相交于P 、Q 两点，求CPQ S ?最大时的直线方程. 椭 圆
Unit 1 1. Although most dreams apparently happen__, dream activity may be provoked by external influences. A. spontaneously B. simultaneously C. homogeneously D. instantaneously 2. She let out a terrified __ when she heard the news of the tragedy happened on September 11 in USA, A. cheer B. yell C. sigh D. curse 3. The ties that bind us together in common activity are so __that they can disappear at any moment. A. trivial B. fatal C. tentative D. feeble 4. She __ the person who was in her way A, swore at B. promised C. swore in D. sworn at 5. Mary made steady __ in English after she put her heart into it. A. advance B. improvement C. progress D. program 6. He is the __ husband for her. A. idea B. ideal C. idle D. idiot 7. We naturally __ the name of Darwin with the doctrine of evolution. A. associate B. vain C. reveal D. worship 8. When we had finished dinner, Mary asked the waiter for the __. A, note B. cheque C. bill D. tip 9. The murderer __ a dagger into her heart. A. plugged B. penetrated C. pressed D. thrust 10. The women were able to equal or __ the men who worked beside them. A. surpass B. exceed C. overtake D. lagged Unit 2 1. For many patients, institutional care is the most __ and beneficial form of care. A. pertinent B. appropriate C. acute D. persistent 2. Several international events in the early 1990s seem likely to ___ , or at least weaken, the trends that emerged in the 1980s. A. revolt B. revolve C. reverse D. revive 3. The elderly Russians find it hard to live on their state __ . A. pensions B. earnings C. salaries D. donations 4. There is no __ attached to what you are doing, so you shouldn' t be ashamed. A. stigma B. enigma C. dilemma D. aroma 5. The boat ___ down the river. A. drifted B. floated C. drove D. drilled 6. The conditions of the contract must be __ exactly. A. achieved B. completed C. fulfilled D. finished 7. One of his eyes was injured in an accident, but after a __ operation, he quickly recovered his sight. A. delicate B. considerate C. average D. general
高中椭圆练习题 一、选择题： 1.下列方程表示椭圆的是（） A.22 199x y += B.2228x y --=- C. 22 1259 x y -= D.22(2)1x y -+= 2.动点P 到两个定点1F （- 4，0）.2F （4，0）的距离之和为8，则P 点的轨迹为（） A.椭圆 B.线段12F F C.直线12F F D.不能确定 3.已知椭圆的标准方程2 2 110 y x +=，则椭圆的焦点坐标为（） A.( B.(0, C.(0,3)± D.(3,0)± 4.椭圆2222 222222 222 11()x y x y a b k a b a k b k +=+=>>--和的关系是 A ．有相同的长.短轴B ．有相同的离心率 C ．有相同的准线 D ．有相同的焦点 5.已知椭圆22 159 x y +=上一点P 到椭圆的一焦点的距离为3，则P 到另一焦点的距离是（） A.3 B.2 C.3 D.6 6.如果22 212 x y a a + =+表示焦点在x 轴上的椭圆，则实数a 的取值范围为（） A.(2,)-+∞ B.()()2,12,--?+∞ C.(,1)(2,)-∞-?+∞ D.任意实数R 7.“m>n>0”是“方程2 2 1mx ny +=表示焦点在y 轴上的椭圆的”（） A.充分而不必要条件 B.必要而不充分条件 C.充要条件 D.既不充分也不必要条件 8.椭圆的短轴长是4，长轴长是短轴长的 3 2 倍，则椭圆的焦距是（） B.4 C.6 D.
2 F C c D 1 F 9.关于曲线的对称性的论述正确的是（） A.方程2 2 0x xy y ++=的曲线关于X 轴对称 B.方程3 3 0x y +=的曲线关于Y 轴对称 C.方程2 2 10x xy y -+=的曲线关于原点对称 D.方程3 38x y -=的曲线关于原点对称 10.方程 22 22 1x y ka kb +=（a ＞b ＞0,k ＞0且k ≠1)与方程22 221x y a b +=（a ＞b ＞0)表示的椭圆（ ）. A.有相同的离心率；B.有共同的焦点； C.有等长的短轴.长轴； D.有相同的顶点. 第11题 二、填空题：（本大题共4小题，共20分.） 11.（6分）已知椭圆的方程为： 22 164100 x y +=，则a=___，b=____，c=____， 焦点坐标为：___ __，焦距等于______;若CD 为过左焦点F1的弦， （如图）则?2F CD 的周长为________. 12.（6分）椭圆2 2 1625400x y +=的长轴长为____，短轴长为____， 焦点坐标为 四个顶点坐标分别为___ ， 离心率为 ；椭圆的左准线方程为 13.（4分）比较下列每组中的椭圆： （1）①2 2 9436x y += 与 ② 22 11216 x y += ，哪一个更圆 （2）① 22 1610 x y +=与②22936x y +=，哪一个更扁 14.（4分）若一个椭圆长轴的长度.短轴的长度和焦距成等差数列， 则该椭圆的离心率是
椭圆常考题型汇总及练习 第一部分：复习运用的知识 （一）椭圆几何性质 椭圆第一定义:平面内与两定点21F F 、距离和等于常数 ()a 2(大于21F F ）的点的轨迹叫做椭圆. 两个定点叫做椭圆的焦点；两焦点间的距离叫做椭圆的焦距 ()c 2. 椭圆的几何性质:以 ()0122 22>>=+b a b y a x 为例 1. 范围: 由标准方程可知，椭圆上点的坐标()y x ,都适合不等式1,122 22≤≤b y a x ，即 b y a x ≤≤,说明椭圆位于直线a x ±=和b y ±=所围成的矩形里（封闭曲线）.该性质主要用 于求最值、轨迹检验等问题. 2. 对称性:关于原点、x 轴、y 轴对称，坐标轴是椭圆的对称轴，原点是椭圆的对称中心。 3. 顶点（椭圆和它的对称轴的交点） 有四个：()()()().,0B ,0B 0,0,2121b b a A a A 、、、-- 4. 长轴、短轴： 21A A 叫椭圆的长轴，a a A A ,221=是长半轴长； 21B B 叫椭圆的短轴，b b B B ,221=是短半轴长. 5. 离心率 （1）椭圆焦距与长轴的比a c e =，()10,0<<∴>>e c a Θ （2）22F OB Rt ?, 2 22 22 22OF OB F B +=，即222c b a +=.这是椭圆的特征三角形，并且 22cos B OF ∠的值是椭圆的离心率. （3）椭圆的圆扁程度由离心率的大小确定，与焦点所在的坐标轴无关.当e 接近于1时，c 越接近于a ，从而22c a b -= 越小， 椭圆越扁；当e 接近于0时，c 越接近于0，从而2 2c a b -=越大，椭圆越接近圆。
九年级下 Unit 4 基础训练 一、语法选择 Campbell Remess is a teenager from Australia. He has been sewing (缝制)teddy bears for sick children __1__ several years. The story __2__ in 2019 when Campbell was nine years old. He told his parents __3__ he wanted to give Christmas gifts to children in hospitals. __4__ his parents said no, because with nine children of their own, buying presents for sick children would just cost too much. However, the little boy didn’t give up. He decided to make their presents by __5__. Campbell made his first teddy bear with his mother's sewing machine in his bedroom. It was __6__ for him as he had never done this before. He downloaded(下载) patterns from the Internet and learned __7__ to make a teddy bear by watching videos online. It took him five hours __8__ his first teddy bear. He __9__ now make a teddy bear in an hour. He has also started a project called “Project 365 by Campbell” in which he tries to make __10__ teddy bear every day. Young Campbell uses his pocket money to buy materials for making teddy bears. To make __11__ pocket money, he helps his parents with housework whenever he is free. Sometimes, he __12__ sells his teddy bears online to raise money for sick children. Many people __13__ by Campbell's story and they give away free materials to him. Campbell __14__ away about 1, 300 teddy bears so far. He is now busy __15__ this year's teddy bears. He said that he had never thought of stopping and he would keep putting smiles on people's faces. 1. A. at B. for C. in D. on 2. A. begin B. begins C. began D. has begun 3. A. that B. what C. whether D. if 4. A. And B. But C. As D. So 5. A. he B. his C. him D. himself 6. A. hard B. harder C. hardest D. hardly 7. A. how B. why C. where D. when 8. A. finish B. finishing C. to finish D. to finshing 9. A. should B. must C. need D. can 10. A. a B. an C. the D. / 11. A. few B. little C. many D. more 12. A. also B. too C. either D. neither 13. A. encouraged B. are encouraged C. have encouraged D. were encouraged 14. A. gives B. has given C. gave D. will give 15. A. make B. made C. making D. to make 二、完形填空
椭圆练习题(经典归纳)标准化文件发布号：（9312-EUATWW-MWUB-WUNN-INNUL-DDQTY-KII
初步圆锥曲线 感受：已知圆O 以坐标原点为圆心且过点12? ?? ,,M N 为平面上关于原点对称的两点,已知N 的坐 标为0,? ?? ,过N 作直线交圆于,A B 两点 （1）求圆O 的方程; （2）求ABM ?面积的取值范围 二. 曲线方程和方程曲线 （1）曲线上点的坐标都是方程的解； （2）方程的解为坐标的点都在曲线上. 三. 轨迹方程 例题：教材 A 组.T3 T4 B 组 T2 练习1.设一动点P 到直线:3l x =的距离到它到点()1,0A 的距离之比为3 ，则动点P 的轨迹方程是____ 练习2.已知两定点的坐标分别为()()1,0,2,0A B -，动点满足条件2MBA MAB ∠=∠，则动点M 的轨迹方程为___________ 总结：求点轨迹方程的步骤： （1）建立直角坐标系 （2）设点：将所求点坐标设为(),x y ，同时将其他相关点坐标化（未知的暂用参数表示） （3）列式：从已知条件中发掘,x y 的关系，列出方程 （4）化简：将方程进行变形化简，并求出,x y 的范围 四. 设直线方程 设直线方程：若直线方程未给出，应先假设. （1）若已知直线过点00(,)x y ，则假设方程为00()y y k x x ； （2）若已知直线恒过y 轴上一点()t ，0，则假设方程为t kx y +=； （3）若仅仅知道是直线，则假设方程为b kx y += 【注】以上三种假设方式都要注意斜率是否存在的讨论； （4）若已知直线恒过x 轴上一点(,0)t ，且水平线不满足条件（斜率为0），可以假设
Unit 1 Where did you go on vacation 一、英汉互译。 1. stay at home ________________________ 2. 去夏令营________________________ 3. go to New York ________________________ 4. 去海滩________________________ 5. visit my uncle ________________________ 6. 去山里________________________ 7. go on vacation ________________________ 8. 参观博物馆________________________ 二．单项选择。 1.It is raining hard outside. You’d better bring _____ umbrella with you .. A. a B. an C. the D. / 2.—Do you know the _____ between these two words? ---Yes ,I do. A. different B. difference C. bicycle D. building 3. ____seems very hard to reach the top of the mountains. A. That B. This C. I D. It 4. The little boy isn’t ______ to pick the apples on the tree. A. short enough B. enough short C. tall enough D. enough tall 5. This is a good chance. Does ____ want to have a try? A. someone B. anyone C. everyone D. no one 6. My parents will be away for a week, I must look after ____ well. A. myself B. me C. my D. mine 7. – Where did you go last vacation? -- I ______. A. go to the beach B. went to doctor C. went to the mountains D. went to school 8. He decided ________ tomorrow morning.
椭圆练习题 一.选择题： １.已知椭圆 上的一点P ，到椭圆一个焦点的距离为３，则P 到另一焦点距离为（ D ） A ．２ B ．３ C ．５ D ．７ ２．中心在原点，焦点在横轴上，长轴长为4，短轴长为２，则椭圆方程是（ C ） A. B. C. D. ３.与椭圆9x 2 +4y 2 =36有相同焦点，且短轴长为4的椭圆方程是( B ) A ４．椭圆的一个焦点是，那么等于（ A ） A. B. C. D. ５．若椭圆短轴上的两顶点与一焦点的连线互相垂直，则离心率等于( B ) A. B. C. D. ６．椭圆两焦点为 ， ，P 在椭圆上，若 △的面积的最大值为12，则椭圆方程为（ B ） A. B . C . D . ７．椭圆的两个焦点是F 1(－1, 0), F 2(1, 0)，P 为椭圆上一点，且|F 1F 2|是|PF 1|与|PF 2| 的等差中项，则该椭圆方程是（ C ）。 A ＋＝1 B ＋＝1 C ＋＝1 D ＋＝1 ８.椭圆的两个焦点和中心，将两准线间的距离四等分，则它的焦点与短轴端点连线的夹角为( C ) (A)450 (B)600 (C)900 (D)120 ９．椭圆 上的点M 到焦点F 1的距离是2，N 是MF 1的中点，则|ON |为（ A ） A. 4 B . 2 C. 8 D . 116 252 2=+y x 22143x y +=22134x y +=2214x y +=22 14 y x +=5185 8014520125201 20 252222222 2=+=+=+=+y x D y x C y x B y x 2 2 55x ky -=(0,2)k 1-1512 21(4,0)F -2(4,0)F 12PF F 221169x y +=221259x y +=2212516x y +=22 1254 x y +=16x 29y 216x 212y 24x 23y 23x 24 y 222 1259 x y +=2 3
椭圆标准方程典型例题 例1 已知椭圆0632 2=-+m y mx 的一个焦点为（0，2）求m 的值． 例2 已知椭圆的中心在原点，且经过点()03， P ，b a 3=，求椭圆的标准方程． 例3 ABC ?的底边16=BC ，AC 和AB 两边上中线长之和为30，求此三角形重心G 的轨迹和顶点A 的轨迹． 例4 已知P 点在以坐标轴为对称轴的椭圆上，点P 到两焦点的距离分别为354和3 52，过P 点作焦点所在轴的垂线，它恰好过椭圆的一个焦点，求椭圆方程． 例5 已知椭圆方程()0122 22>>=+b a b y a x ，长轴端点为1A ，2A ，焦点为1F ，2F ，P 是椭圆上一点，θ=∠21PA A ，α=∠21PF F ．求：21PF F ?的面积（用a 、b 、α表示）． 例6 已知动圆P 过定点()03，-A ，且在定圆()64322=+-y x B ：的内部与其相内 切，求动圆圆心P 的轨迹方程 例7 已知椭圆1222=+y x ，（1）求过点?? ? ??2121，P 且被P 平分的弦所在直线的方程；
（2）求斜率为2的平行弦的中点轨迹方程； （3）过()12， A 引椭圆的割线，求截得的弦的中点的轨迹方程； （4）椭圆上有两点P 、Q ，O 为原点，且有直线OP 、OQ 斜率满足21-=?OQ OP k k ， 求线段PQ 中点M 的轨迹方程． 例8 已知椭圆1422=+y x 及直线m x y +=． （1）当m 为何值时，直线与椭圆有公共点？ （2）若直线被椭圆截得的弦长为 5 102，求直线的方程． 例9 以椭圆13 122 2=+y x 的焦点为焦点，过直线09=+-y x l ：上一点M 作椭圆，要使所作椭圆的长轴最短，点M 应在何处？并求出此时的椭圆方程． 已知方程1352 2-=-+-k y k x 表示椭圆，求k 的取值范 例10 已知1cos sin 2 2=-ααy x )0(πα≤≤表示焦点在y 轴上的椭圆，求α的取值范围． 12 求中心在原点，对称轴为坐标轴，且经过)2,3(-A 和)1,32(-B 两点的椭圆方程．
谷城三中高一英语必修（一）Unit 4基础训练 一、单词拼写 1. After ________(电) was cut off, the lights went out. 2．The audience ________(爆发) into cheers. 3．We were ________(震惊) at the bad news. 4．The flood ________(毁坏) a lot of houses and many people became homeless. 5．The people ________(受伤) in the accident were sent to hospital without delay. 6．Fires, floods and earthquakes are __________(灾难)． 7．Many men were________(埋葬)underground when the accident at the mine happened. 8．Trees along the road provide ________(掩蔽处) from the sun for the farmers. 9．The ________(受惊的) girl was speechless after she saw the terrible scene. 10．The bridge was badly ________(损坏) by the flood. 11．The boiling kettle(水壶) was giving off ________(蒸汽)． 12．The workers are ________(挖) a well in the desert. 13．The park is beautiful，________(尤其是) in spring. 14．His views have been ________ (表达) in numerous speeches. 15．I can't ________ (判断) whether he is right or wrong. 16．Give Marie my ________ (祝贺) and tell her I'll come soon. 17．I ________ (真诚地) hope I'll see her again. 18．You should draw up a plan or ________ (大纲) for the essay. 二、选词填空(who, whom, whose, that, which) 1．The house ________ we live in is very small. 2．This is the best TV play ________ I've ever watched. 3．The only thing ________ I can remember is the big fire. 4．Is there anything ________ you want to buy? 5．He asked about the factories and workers ________ we had just visited. 6．The girl ________ hair is golden is from England. 7．Our school is not the one ________ it used to be. 8．My grandparents live in a house ________ was built 20 years ago. 9．I have a friend ________ likes listening to classical music. 10．Yesterday, Emily was wearing the new dress ________ I gave to her. 11．This is the scientist ________ name is known all over the country. 12．Do you still remember the chicken farm ________ we visited three months ago? 13．Some countries ________ names I had never heard of before were shown on the map. 14．Anyone ________ failed to come to the meeting yesterday must give his reason. 15．On the train I saw a girl ________ you worked with. 16．The pen ________ he bought yesterday is the same as mine. 三、单句语法填空 1．People were ________ (shock) by the eruption of the volcano, for it was even greater than they had expected. 2．He was dead and ________ (bury) at the top of the hill. 3．The child was ________ (frighten) by the ghost story. 4．An old Roman vase was ________ (dig) up here last month. 5．It made the headlines in the ________ (nation) newspapers. 6．________ (judge) by what everyone says about him, he has a good chance of winning. 7．Luckily, the traffic accident didn't do much damage ________ either of the cars. 8．— Can you introduce yourself to others in English? — Sorry. I can't express ________ (me) in English. Chinese, OK? 9．He is ________ of his daughter, which makes his daughter become too ________ of herself and finally this ________ ruined her. (proud) 10．He ________ his thanks to us, with a thankful ________ on his face. (express) 11．Ten more deaths had been dug ________ by the time the chairman arrived. 12．A great number of tents were built ________ the survivors. 13．All of a sudden, the huge building lay ________ ruins. 14．He thought little of his daughter's illness and fell fast asleep ________ usual. 15．You must come to the ceremony ________ that special day. 课文缩写语法填空（一） At about 3：00 a．m. on July 28, 1976, people in Tangshan, Hebei Province, woke up and saw bright lights in the sky. They didn't pay much attention and went back to bed as __1__ that night. At 3：42 a．m. everything began to shake. Eleven kilometers __2__(direct) below the city the __3__(great) earthquake of the 20th century began. It was heard in Beijing, __4__ is more than two hundred kilometers away. In fifteen terrible seconds a large city lay __5__ ruins. Two-thirds of the people died or were __6__(injure) during the earthquake. The survivors couldn't believe it was natural. Nearly everything __7__ (destroy). Most of the buildings were gone and many farm animals died. Then later that afternoon, __8__ big quake shook Tangshan. Some rescue workers and doctors __9__(trap) under the ruins. Not all hope was lost. The army sent 150,000 soldiers to Tangshan. Hundreds of thousands of people were helped. Slowly, the city began __10__(breathe) again.