问题导学类比用方程研究椭圆双曲线几何性质的过程与方法,y2 = 2px (p>0)你认为应研究抛物线的哪些几何性质,如何研究这些性质?1. 范围抛物线 y2 = 2px (p>0) 在 y 轴的右侧,开口向右,这条抛物线上的任意一点M 的坐标 (x, y) 的横坐标满足不等式 x ≥ 0;当x 的值增大时,|y| 也增大,这说明抛物线向右上方和右下方无限延伸.抛物线是无界曲线.2. 对称性观察图象,不难发现,抛物线 y2 = 2px (p>0)关于 x 轴对称,我们把抛物线的对称轴叫做抛物线的轴.抛物线只有一条对称轴. 3. 顶点抛物线和它轴的交点叫做抛物线的顶点.抛物线的顶点坐标是坐标原点 (0, 0) .4. 离心率抛物线上的点M 到焦点的距离和它到准线的距离的比,叫做抛物线的离心率. 用 e 表示,e = 1.探究如果抛物线的标准方程是〖 y〗^2=-2px(p>0), ②〖 x〗^2=2py(p>0), ③〖 x〗^2=-2py(p>0), ④
二、直线与抛物线的位置关系设直线l:y=kx+m,抛物线:y2=2px(p>0),将直线方程与抛物线方程联立整理成关于x的方程k2x2+2(km-p)x+m2=0.(1)若k≠0,当Δ>0时,直线与抛物线相交,有两个交点;当Δ=0时,直线与抛物线相切,有一个切点;当Δ<0时,直线与抛物线相离,没有公共点.(2)若k=0,直线与抛物线有一个交点,此时直线平行于抛物线的对称轴或与对称轴重合.因此直线与抛物线有一个公共点是直线与抛物线相切的必要不充分条件.二、典例解析例5.过抛物线焦点F的直线交抛物线于A、B两点,通过点A和抛物线顶点的直线交抛物线的准线于点D,求证:直线DB平行于抛物线的对称轴.【分析】设抛物线的标准方程为:y2=2px(p>0).设A(x1,y1),B(x2,y2).直线OA的方程为: = = ,可得yD= .设直线AB的方程为:my=x﹣ ,与抛物线的方程联立化为y2﹣2pm﹣p2=0,
二、典例解析例4.如图,双曲线型冷却塔的外形,是双曲线的一部分,已知塔的总高度为137.5m,塔顶直径为90m,塔的最小直径(喉部直径)为60m,喉部标高112.5m,试建立适当的坐标系,求出此双曲线的标准方程(精确到1m)解:设双曲线的标准方程为 ,如图所示:为喉部直径,故 ,故双曲线方程为 .而 的横坐标为塔顶直径的一半即 ,其纵坐标为塔的总高度与喉部标高的差即 ,故 ,故 ,所以 ,故双曲线方程为 .例5.已知点 到定点 的距离和它到定直线l: 的距离的比是 ,则点 的轨迹方程为?解:设点 ,由题知, ,即 .整理得: .请你将例5与椭圆一节中的例6比较,你有什么发现?例6、 过双曲线 的右焦点F2,倾斜角为30度的直线交双曲线于A,B两点,求|AB|.分析:求弦长问题有两种方法:法一:如果交点坐标易求,可直接用两点间距离公式代入求弦长;法二:但有时为了简化计算,常设而不求,运用韦达定理来处理.解:由双曲线的方程得,两焦点分别为F1(-3,0),F2(3,0).因为直线AB的倾斜角是30°,且直线经过右焦点F2,所以,直线AB的方程为
1.判断 (1)椭圆x^2/a^2 +y^2/b^2 =1(a>b>0)的长轴长是a. ( )(2)若椭圆的对称轴为坐标轴,长轴长与短轴长分别为10,8,则椭圆的方程为x^2/25+y^2/16=1. ( )(3)设F为椭圆x^2/a^2 +y^2/b^2 =1(a>b>0)的一个焦点,M为其上任一点,则|MF|的最大值为a+c(c为椭圆的半焦距). ( )答案:(1)× (2)× (3)√ 2.已知椭圆C:x^2/a^2 +y^2/4=1的一个焦点为(2,0),则C的离心率为( )A.1/3 B.1/2 C.√2/2 D.(2√2)/3解析:∵a2=4+22=8,∴a=2√2.∴e=c/a=2/(2√2)=√2/2.故选C.答案:C 三、典例解析例1已知椭圆C1:x^2/100+y^2/64=1,设椭圆C2与椭圆C1的长轴长、短轴长分别相等,且椭圆C2的焦点在y轴上.(1)求椭圆C1的半长轴长、半短轴长、焦点坐标及离心率;(2)写出椭圆C2的方程,并研究其性质.解:(1)由椭圆C1:x^2/100+y^2/64=1,可得其半长轴长为10,半短轴长为8,焦点坐标为(6,0),(-6,0),离心率e=3/5.(2)椭圆C2:y^2/100+x^2/64=1.性质如下:①范围:-8≤x≤8且-10≤y≤10;②对称性:关于x轴、y轴、原点对称;③顶点:长轴端点(0,10),(0,-10),短轴端点(-8,0),(8,0);④焦点:(0,6),(0,-6);⑤离心率:e=3/5.
二、典例解析例5. 如图,一种电影放映灯的反射镜面是旋转椭圆面(椭圆绕其对称轴旋转一周形成的曲面)的一部分。过对称轴的截口 ABC是椭圆的一部分,灯丝位于椭圆的一个焦点F_1上,片门位另一个焦点F_2上,由椭圆一个焦点F_1 发出的光线,经过旋转椭圆面反射后集中到另一个椭圆焦点F_2,已知 〖BC⊥F_1 F〗_2,|F_1 B|=2.8cm, |F_1 F_2 |=4.5cm,试建立适当的平面直角坐标系,求截口ABC所在的椭圆方程(精确到0.1cm)典例解析解:建立如图所示的平面直角坐标系,设所求椭圆方程为x^2/a^2 +y^2/b^2 =1 (a>b>0) 在Rt ΔBF_1 F_2中,|F_2 B|= √(|F_1 B|^2+|F_1 F_2 |^2 )=√(〖2.8〗^2 〖+4.5〗^2 ) 有椭圆的性质 , |F_1 B|+|F_2 B|=2 a, 所以a=1/2(|F_1 B|+|F_2 B|)=1/2(2.8+√(〖2.8〗^2 〖+4.5〗^2 )) ≈4.1b= √(a^2 〖-c〗^2 ) ≈3.4所以所求椭圆方程为x^2/〖4.1〗^2 +y^2/〖3.4〗^2 =1 利用椭圆的几何性质求标准方程的思路1.利用椭圆的几何性质求椭圆的标准方程时,通常采用待定系数法,其步骤是:(1)确定焦点位置;(2)设出相应椭圆的标准方程(对于焦点位置不确定的椭圆可能有两种标准方程);(3)根据已知条件构造关于参数的关系式,利用方程(组)求参数,列方程(组)时常用的关系式有b2=a2-c2等.
二、探究新知一、空间中点、直线和平面的向量表示1.点的位置向量在空间中,我们取一定点O作为基点,那么空间中任意一点P就可以用向量(OP) ?来表示.我们把向量(OP) ?称为点P的位置向量.如图.2.空间直线的向量表示式如图①,a是直线l的方向向量,在直线l上取(AB) ?=a,设P是直线l上的任意一点,则点P在直线l上的充要条件是存在实数t,使得(AP) ?=ta,即(AP) ?=t(AB) ?.如图②,取定空间中的任意一点O,可以得到点P在直线l上的充要条件是存在实数t,使(OP) ?=(OA) ?+ta, ①或(OP) ?=(OA) ?+t(AB) ?. ②①式和②式都称为空间直线的向量表示式.由此可知,空间任意直线由直线上一点及直线的方向向量唯一确定.1.下列说法中正确的是( )A.直线的方向向量是唯一的B.与一个平面的法向量共线的非零向量都是该平面的法向量C.直线的方向向量有两个D.平面的法向量是唯一的答案:B 解析:由平面法向量的定义可知,B项正确.
跟踪训练1在正方体ABCD-A1B1C1D1中,E为AC的中点.求证:(1)BD1⊥AC;(2)BD1⊥EB1.(2)∵(BD_1 ) ?=(-1,-1,1),(EB_1 ) ?=(1/2 "," 1/2 "," 1),∴(BD_1 ) ?·(EB_1 ) ?=(-1)×1/2+(-1)×1/2+1×1=0,∴(BD_1 ) ?⊥(EB_1 ) ?,∴BD1⊥EB1.证明:以D为原点,DA,DC,DD1所在直线分别为x轴、y轴、z轴,建立如图所示的空间直角坐标系.设正方体的棱长为1,则B(1,1,0),D1(0,0,1),A(1,0,0),C(0,1,0),E(1/2 "," 1/2 "," 0),B1(1,1,1).(1)∵(BD_1 ) ?=(-1,-1,1),(AC) ?=(-1,1,0),∴(BD_1 ) ?·(AC) ?=(-1)×(-1)+(-1)×1+1×0=0.∴(BD_1 ) ?⊥(AC) ?,∴BD1⊥AC.例2在棱长为1的正方体ABCD-A1B1C1D1中,E,F,M分别为棱AB,BC,B1B的中点.求证:D1M⊥平面EFB1.思路分析一种思路是不建系,利用基向量法证明(D_1 M) ?与平面EFB1内的两个不共线向量都垂直,从而根据线面垂直的判定定理证得结论;另一种思路是建立空间直角坐标系,通过坐标运算证明(D_1 M) ?与平面EFB1内的两个不共线向量都垂直;还可以在建系的前提下,求得平面EFB1的法向量,然后说明(D_1 M) ?与法向量共线,从而证得结论.证明:(方法1)因为E,F,M分别为棱AB,BC,B1B的中点,所以(D_1 M) ?=(D_1 B_1 ) ?+(B_1 M) ?=(DA) ?+(DC) ?+1/2 (B_1 B) ?,而(B_1 E) ?=(B_1 B) ?+(BE) ?=(B_1 B) ?-1/2 (DC) ?,于是(D_1 M) ?·(B_1 E) ?=((DA) ?+(DC) ?+1/2 (B_1 B) ?)·((B_1 B) ?-1/2 (DC) ?)=0-0+0-1/2+1/2-1/4×0=0,因此(D_1 M) ?⊥(B_1 E) ?.同理(D_1 M) ?⊥(B_1 F) ?,又因为(B_1 E) ?,(B_1 F) ?不共线,因此D1M⊥平面EFB1.
The topic of this part is “Write about your festival experience”.During the Listening and Speaking and Talking, students are just asked to say out their festival experiences such as the Spring Festival, Mid-autumn Day, but this part students will be asked to write down their own festival experiences. During the reading part, it introduces the Naadam Festival in Inner Mongolia Autonomous Region, which can give students a good example to imitate. Students not only learn the festival, but touch and feel the Inner Mongolian’s character, the spirit and cultural atmosphere, which can help students form the cultural awareness and learn to enjoy and value the diversity of Chinese culture.Concretely, the dairy tells the experience that the author spent the Naadam Festival in Inner Mongolia Autonomous Region with his/her friend. The structure is clear. In the opening paragraph, it introduces the topic of the Naadam Festival and the whole feeling. Then it introduces the items of the festival like the ceremony, wrestling and horse racing. Finally, it summarizes this experience. Because this part is a travel journal, we must guide students pay more attention to these details: 1. use the first person. 2. use the past tense to tell the past thing and use the present or future tense to describe the scenery. 3. use the timeline to tell the development. 4. be careful for the author’s psychology, emotion and feeling, etc.1. Read quickly to get main idea; read carefully to get the detailed information about Naadam Festival.2. Learn the structure of the reading article and language.3. Write an article about a festival experience4. Learn to use the psychology, emotions and feeling in the writing.1. Write an article about a festival experience.2. Use the structure of the reading article and language.
Listening and Speaking introduces the topic of “talking about how to become an astronaut”. This period is aimed to inform students some details about the requirements of being an astronaut. Students can be motivated and inspired by the astronauts. Teachers ought to encourage students to learn from them and let them aim high and dream big.Listening and Talking introduces the theme of "talk about life in space". This part also informs students more details about life in space and can inspire students to be curious about this job. 1. Guide students to listen for numbers concerning dates, years and ages etc2. Cultivate students' ability to talk about how to become an astronaut and life in space ; 3. Instruct students to use functional sentences of the dialogue such as “ first of all, I am not sure, so what might be .. I guess.. I wonder…I am curious…)appropriately.1. Guide students to understand the content of listening texts in terms of the whole and key details; 2. Cultivate students' ability to guess the meaning of words in listening; discuss with their peers how to become a qualified astronaut and describe the life in space.Part 1: Listening and SpeakingStep 1: Lead inPredictionThe teacher can ask students to predict what the listening text is about by looking at the pictures.About how to become an astronaut./the requirements of an astronautStep 2: Then, play the radio which is about an interview a. And after finishing listening for the first time, the students need to solve the following tasks.
Q4: What is the function of the International exploration ?Having astronauts from different countries on boardQ5: What can you learn from Para 4 ?China has made great achievements in exploring spaceQ6: What is the attitude to the space exploration ?SupportiveStep 6 Post reading---RetellPeople have always wanted to learn more about space. Before the mid-20th century, most people felt (1)_________ (travel) into space was an impossible dream. However, (2)____ the help of scientists, peoplesucceeded in realizing their dream (3) _________ (explore) space. On 4 October 1957, the Sputnik 1 satellite (4) ____________(launch) by the USSR. (5) ________________ scientists try to make sure nothing goes wrong, accidents can still happen. These disasters made everyone(6)___________(disappoint), but people still believe in the importance of (7) ________(carry) on space exploration. In 2003, China became the third country to (8)_____________ (independent) send humans into space. Then Shenzhou 6 and 7 completed (9)____ second manned orbit and the first Chinese spacewalk. In spite of the difficulties, scientists hope future (10)__________ (discovery) will not only enable us to understand the universe but also help us survive well into the future.Answers: 1. travelling 2. with 3. to explore 4. was launched 5. Although6. disappointed 7. carrying 8. independently 9. a 10. discoveriesStep 6 Post reading---Critical thinkingQ1: What do you think of the space exploration ? I think it is beneficial to us. Through further study of space, people will make full use of it in the future, such as the space experiments by Wang Yaping in Tian Gong 1.Q2: If you are determined to be an astronaut, what should you prepare at present ?First of all, I should study hard to get a related college degree. Besides, I must keep mental and physical healthy.Step 7. HomeworkTry to summarize the structure of the article by a mind map.
另一方面,其余的人反对这个计划,因为它可能会导致一些不好的影响。7.I hold the belief that space exploration not only enable us to understand how the universe began but also help us survived well into the future.我坚信探索太空不仅能够使我们了解宇宙的起源而且能够帮助我们更好地走进未来。8.I think we should spend more time and money exploring space so as to provide new and better solutions to people's shortterm and longterm problems.为了给人类的短期和长期问题提供更新和更好的解决方法,我认为我们应该花更多的时间和金钱来探索太空。9.From my point of view,it is wrong of young people to depend on their telephones too much,which may do harm to both their physical and mental health.在我看来,年轻人过度依赖手机是不对的,因为它们可能会对他们的身心健康都有害。最近你班同学就“人类是否应该进行宇宙探索”这个问题进行了激烈的讨论。有人认为,探索宇宙不仅让人类更好地了解宇宙的发展,还可以用来指导农业生产,以及把一些探索太空的高新技术用于现实生活;也有一些人认为探索太空花掉了大量的人力物力;影响了人们的生活水平。请你根据以下情况写一篇报告并发表自己的观点。注意:1.写作内容应包括以上全部要点,可适当发挥,使上下文连贯;
Everybody wants to get wealth.In today’s material world,making money or becoming wealthy symbolizes a person’s success and capability. Many people just make every effort, pay any price to attain greater wealth. With money,they can buy nice, large apartments in nice neighborhood. With money they can own luxurious cars. Wealth seems to bring all happiness in life.But is wealth the only road to happiness? Not really. There are many things in the world, which are beyond the means of money, such as friendship, love, health and knowledge. People are so preoccupied with struggling for money that they have no time or would not take the time to form or maintain friendship. What happiness can they feel living as lonely miserable creatures without love or friends in the world even if they accumulate tremendous wealth?In my opinion, people can’t do anything without money, but money is not everything. What money will bring you depends on your personal belief and goal in life. If you are kind enough to help others, especially the poor, money is a good thing to you. With it, you can do much more for the benefit of people and your country, and it will add to your own happiness. If you want money just for your own needs, you’ll never be satisfied or happy. In a word,you should have money spent for more people. Only then can money be the source of your happiness.Step 8 Homework4 students in a group, one acts Roderick, one Oliver, one servant and the fourth one acts Henry Adams, then listen to the tape, pay more attention to the difference between American English and British English in pronunciation, stress, tone.
【参考范文】Narrator:(Henry is smiling as he leaves the restaurant. As he is walking down the street, he sees a sign for a place that cuts hair. He decides to get it cut. )H=Henry;B=Barber;R=rude manH:Good afternoon, I'd like to get a cut, if I may. (The barber looks at Henry's hair and continues cutting another man's hair. )Er, I'd really like a haircut. As you can see it's much too long. B:(in a rude manner) Yes, I can see that. Indeed, I can. H:Fine, well I'll have a seat then. (He sits in one of the barber's chairs. The barber turns to look at Henry. )B:It's quite expensive here, you know!Are you sure you can afford it?H:Yes. I think so. (In comes the rude man. )R:Hey you there. I need a haircut quickly. Can you do me straightaway?B:All right, then, get in the chair and I'll see what I can do. R:Thank you. (sits down in one of the barber's chairs)H:Excuse me, but I was here first. Aren't you going to do my hair first?B:This man's in a hurry. H:Well so am I!I insist that you cut my hair first. B:OK, but I'll have to be quick. This gentleman is waiting. H:Thank you. (They both become quiet. After his hair is cut, the barber tells Henry how much he must pay. Henry shows the barber the bank note. )B:Why, Mr . . . (looks shocked)H:Adams. Henry Adams. I'm sorry, I don't have any change. R:You're that Mr Adams! Well,I'm glad I waited or I might never have known it was you. B:Why, Mr Adams, please don't worry!(wearing a big smile) Nothing to worry about!Nothing at all!Please come back any time, even if you only need too little hairs cut!It will be my honour to serve you!
一、基本情况xxxx年我县通过,公开、公平、公正的方法,按照上级文件和《xx县xxxx年全县农民培训工作方案的通知》(x农字(xxxx)xxx号)的要求,遴选了xx县旅游工业中等专业学校为培训工作的第三方,确定了培训对象为家庭农场主、农民合作社带头人、种养大户。按照工作方案要求,已全部完成任务,即经营管理型xxx人,技能服务型xx人,共计培训xxx人。二、项目组织开展情况(一)领导重视。按照省、市文件精神,我县各级领导对高素质农民培育工作非常重视,县成立高素质农民培育工作领导小组。在高素质农民培育过程中,县农业农村局长到实训现场指导培训工作。(二)精准遴选培育对象。根据《xx县xxxx年高素质农民培训工作实施方案》,认真开展了培训对象的遴选。重点面向家庭农场主、农民合作社带头人和种养大户,统筹推进新型农业经营和服务主体能力提升、种养加能手技能培训、农村创新创业者培养、乡村治理及社会事业发展带头人培育等行动,大力培养高素质农民队伍。
(一)“一单两库一细则”建立情况根据“放管服”改革要求,我局持续对现有法律法规规章规定的检查事项进行梳理,于20xx年建设完善了线上及线下“一单两库一细则”,将法定的检查事项全部纳入随机抽查事项清单,做到“清单之外无检查”;将全市所有具有执法资格的执法人员、市场主体全部纳入双随机范围,做到“应入尽入无例外”;实现了检查事项、检查对象和检查人员“三个全覆盖”。线上依托市场信息系统,及时维护更新检查人员和市场主体信息,实时更新“两库”;线下指定专人负责,及时动态调整更新检查、执法对象名录,确保抽取科学性、合法性。(二)抽查模式、工作安排及执行情况目前我局在抽查模式分为线上、线下两种抽查模式,每月初由各具体执行部门,科学制定抽查计划,当月完成随机检查任务。
1、教材的地位和作用本章教材是初中数学八年级第十四章的内容,是初中数学的重要内容之一。一方面,这是在学习了函数概念的基础上,对函数知识的进一步深入和拓展;另一方面,又为学习反比例函数、二次函数等知识奠定了基础,是进一步研究数学应用的工具性内容。鉴于这种认识,我认为,本节课不仅有着广泛的实际应用,而且起着承前启后的作用。 2、学情分析针对即将面临中考的学生来说,在具有了一定知识的基础上,培养他们分析问题和解决问题的能力尤为重要,因此本节课除了让学生进一步熟悉本章知识以外,重在培养学生的能力。从认知状况来说,学生在此之前已经学习了函数的定义,对函数的三种表示法已经有了初步的认识,这为顺利完成本节课的教学任务打下了基础,但对于一次函数的性质的理解和应用,仍然是部分学生所存在的困惑,所以在教学过程中要充分利用一些函数的图象,通过直观教学让学生更加深入的理解一次函数的性质。
1、教材的内容、地位和作用氯气选自高 中化学第一册第四章第一节,这一课题包括两部分内容,第一部分主要介绍氯气的性质和用途第二部分主要介绍氯气的实验室制法以及氯离子的检验氯是比较典型的非金属元素,氯及氯的化和物在日常生活、工农业中的应用非常广泛对氯气性质、用途和制法的研究,不仅是下一节进一步学习、研究卤素性质相似性及其变化规律的需要,也是研究同族元素 性质变化规律的需要由于高中阶段对氯气的性质、用途等介绍、应用较多,对学生全面认识化学元素、形成正确观点、掌握正确学习方法等有重要作用
2.情境体验“生活中不经意间就会造成浪费,请同学们先看下面一些数字。”课件出示一组数据,通过一连串的数字让孩子们在强烈的震撼中感受到节俭的重要性。“多么惊人的数字,让我们深刻地反思自己的行为。再来看看他们的做法,你认同吗?如果是你,你会怎么做。”课件展示三个情境图,学生体会。特别在展示第三组图片时,在音乐下我深情并茂地讲述:“简陋的校舍,狭小的教室,粗糙的课桌椅,凹凸不平的黑板……有的甚至教室都没有!西南地区上,干涸的双唇、裂开的土地、夹杂泥沙的饮用水,多么地让人心痛!我们在浪费的同时,他们却是那么的渴望!同学们,看了这三组情境图,说说你的想法?”鼓励学生畅所欲言,发表意见。本环节中,我通过调查分析——谈感想——观看数字—看图——比较——再谈感想的过程,让学生把节约意识渗透到现实生活中,懂得节约应从小事做起,从一点一滴做起。
(五)课堂小结四、说班会过程:(一)谈话导入:小朋友们,你知道世界上最珍贵的是什么吗?(生命)当有同学回答说是生命时,师说:“对,就是生命!生命对于我们每个人来说只有一次,所以生命是最可贵的,但是它又是最脆弱的,有时会在那不经意的一瞬间,生命的泉水便会永远消失,所以,本次班队课,老师想和你们一起讨论一下如何爱惜生命、注意安全。”(二)出示一些安全事故的资料 视频和图片资料师过渡:近些年来,发生在学生中的安全事故很多,造成了多少学生死亡,拆散了多少个幸福的家庭,使多少父母痛不欲生!下面请同学们看看这些视频和图片资料(以上设计意图是通过学生视觉和听觉的感官,切身感受生命很脆弱、安全很重要,激发他们提高安全意识)
【总结讲解】地球为生命物质的存在提供了三个最优越的条件,这也是其它行星不具备的条件——(1)日地距离适中(1.496亿km),使地表平均气温为15℃,有利于生命过程的发生和发展;地球上的温度,还有利于水的液态存在。适合生物呼吸的大气: (2) 地球的体积、质量适中,吸引大量气体聚集在地球周围,又经过漫长的演化,形成了以氮、氧为主的适合生物呼吸的大气。(3)海洋的形成: 由于地球内部放射性元素衰变致热和原始地球重力收缩及地球内部的物质运动等形成了原始大洋,地球最初的单细胞生命就出现在大洋中。(备注:此部分可以模拟演示或讲解地球存在生命的温度、大气、水等条件;假设地球温度过高或过低对地球生命的影响;引导学生分析地球大气、温度与地球水的关系)【板书】1、日地距离适中2、地球的体积、质量适中3、液态水的存在【启发提问】 宇宙中是否只有地球上存在有生命物质?