问题 解答题

一直线过抛物线y2=2px(p>0)的焦点F,且交抛物线于A,B两点,C为抛物线准线的一点.

(1)求证:∠ACB不可能是钝角;

(2)是否存在这样的点C,使得△ABC为正三角形?若存在,请求出点C的坐标;若不存在,请说明理由.

答案

解:设

直线AB方程为

,得:y2﹣2pty﹣p2=0,

不可能为钝角,

故∠ACB不可能是钝角

(2)假设存在点C,使得△ABC为正三角形

由(1)得:线段AB的中点为

①若直线AB的斜率不存在,这时t=0,

点C的坐标只可能是

,得:,矛盾,

于是直线AB的斜率必存在.

②由CM⊥AB,得:kCMkAB=﹣1,

∴m=pt3+2pt,

,|AB|=2p(t2+1),

,得:

故存在点,使得△ABC为正三角形.

阅读理解与欣赏

飞机黑匣子

①现代民航客机尽管采用大量新技术,采取许多安全防范措施,但意外坠机事件仍在所难免。一旦发生空难,人们总是千方百计寻找黑匣子,从中分析事故原因。

②黑匣子是一种飞行记录仪。它记录下飞行中的重要参数,例如,飞机相对地面状态、速度、高度、航向、航速、燃料等等。依照这些参数,就可以很容易标绘出航迹。信息随录随洗,但保留飞机失事前数小时的飞行信息。

③其实黑匣子并非黑色,而是桔红色。它之所以采用桔红色,主要为了与周围地形地貌颜色相区别,便于搜寻。除了桔红色外表外,为了更容易找到它,黑匣子还装有无线电信标,这种装置能自动、定时向外发射一定的无线电信号,便于专用的接收机接收。

④黑匣子外壳十分坚固。它能同时承受来自三个方向3.4公斤重的物体长达5分钟的撞击;能承受一件230公斤的重物从3米高度砸下的冲击;黑匣子表面覆涂隔热材料,能经受起火爆炸,并能在1100℃的烈火中烧半小时;能在3米深的水中浸泡30天。所以,在飞机遭遇不幸后,黑匣子往往是唯一的“幸存者”。

⑤为了保证黑匣子能正常工作,与所有航空航天设计一样,它在工作程序和故障考虑上有很高的“自保性”和“互保性”。这点好比进入银行金库的规章制度一样,目的是为了万无一失。例如黑匣子的电源供给很特殊。在正常情况下,黑匣子所需的直流电由飞机的发电系统供给。这种发电机是交直流变换机,将发出的交流电直接由直流电机变换成直流电。而一旦发电机出故障时,立即自动切换成由蓄电池供电,提供所需的电压。又如黑匣子的工作开关一般在飞机发动前应接通,但即使驾驶员忘记了也无妨。当飞机在跑道上滑行到一定速度后,起落架自动收回,黑匣子的工作开关因起落架支柱的压力而自动接通。

⑥目前正在研制中的黑匣子将趋于微型计算机化。这个电子装置被装在一个保护匣内,它由采集数据的接口卡片、存储器和把信息编入存储器的程序三个主要部分组成。它与传统的黑匣子相比有很大优越性,例如,它可以变换参数记录速度,当一出现不正常时,便自动加快记录速度,以备人们更加准确地进行分析,此外,它的体积也将被大大缩小。

小题1:本文说明对象是       。文章先介绍黑匣子的定义,然后从                    等三个方面分别说明黑匣子的特点,最后阐述了黑匣子的发展趋势。(4分)

小题2:根据下列材料的要点,为“黑匣子”下定义。(4分)

①黑匣子用来记录飞机飞行中的各种资料

②飞机失事后可以依据黑匣子的记录分析飞机失事的原因

③黑匣子是一种飞行记录仪

④黑匣子装在飞机的座舱里

小题3:第④段加点词“往往”能否删去?为什么?(4分)

小题4:第⑤段主要运用了举例子的说明方法,共列举了两个例子,这两个例子能否删掉一个?请说说理由。(6分)

阅读理解

任务型阅读 

     阅读下列材料,从所给的六个选项(A、B、C、D、E和F)中选出符合各小题要求的最佳选项,选项中有一项为多余选项。

     Directions:  Read the following text and choose the most suitable heading from A-F for each

paragraph.  There is one extra heading which you do not need.

1._____

     The colored part of the eye is called the iris. There are three basic eye colours ─ brown, blue and

green. A few albino people have red or pink eyes, but these are very rare. Many people believe that

blue eyes are more delicate than brown eyes. In fact they are just as tough as brown eyes, although they

are more sensitive to light.

2.______

We only see part of the eyeball, although the whole eye is as big as a table tennis ball. Light enters the eye

through the pupil and passes through the lens. The lens focuses the light onto the retina at the back of the

eye. The retina sends the signal to the brain along the optic nerve. The image on the retina is actually

upside-down, but the brain corrects it. As we get older our eyesight becomes worse. This happens

because the lens isn't as flexible as when we are young and the eye muscles are weaker.

3._____

     Our eyes are the most important of our five senses. We receive 80% of our information about the

world through our eyes. We also send signals to other people with our eyes. Some eye signals are

unconscious. When we look at something nice, our pupils get bigger. But when we don't like something,

they become smaller. We cry when we are unhappy and sometimes when we are very happy. But we

can also control some eye signals. For example, we can wink at someone or raise an eyebrow.

Sunglasses make someone appear mysterious or dangerous, because they hide that eyes and so we can't

see the signals.

4._____  

     We find large eyes more attractive. Children have large eyes in proportion to their heads. Cartoon

characters always have large eyes, too. We can't actually change our eyes, but we can make them look

bigger with make-up. Eye make-up isn't new. Pictures in the Pyramids show that the ancient Egyptians

both men and women-used it. False eyelashes can make eyelashes longer. Eye shadow on the eyelids

can make the eyes look bigger and more dramatic.Glasses can also make eyes look bigger.

5. _______

      We do not normally look into someone's eyes for long, especially when they are very close. Eye

contact can be very threatening, so people only do it when they want to threaten someone. It is also

very intimate. This is why lovers gaze into each other's eyes. It's also why people don't look at each

other in lifts.

A. Ways to beautify eyes

B. Proper use of eye contact

C. Techniques of sending eye signals

D. Colours of people's eyes

E. Functions of different parts of the eye

F. Variety of messages conveyed through