问题 解答题

抛物线顶点在原点,焦点在x轴上,且过点(8,8),焦点为F

(1)求抛物线的焦点坐标和标准方程;

(2)P是抛物线上一动点,M是PF的中点,求M的轨迹方程.

答案

(1)抛物线顶点在原点,焦点在x轴上,且过点(8,8),

设抛物线解析式为y2=2px,把(8,8)代入,得,64=2×8p,∴p=4

∴抛物线标准方程为:y2=8x,焦点坐标为F(2,0)

(2)设M(x,y),P(x0,y0),

x=
x0+2
2
y=
y0
2
x0=2x-2
y0=2y

又∵

y20
=8x0

∴(2y)2=8(2x-2)

∴y2=4(x-1)

∴M的轨迹方程为y2=4x-4.

阅读理解

Most people want to know how things are made. They honestly admit, however, that they hardly know a thing when it comes to understanding how a piece of music is made. Where a composer begins, how he manages to keep going – in fact, how and when he learns his trade – all are covered in complete darkness. The composer, in short, is a man of mystery .

One of the first things the common man wants to know about is the part inspiration plays in a composer’s work. He finds it difficult to believe that composers are not much interested in that question. Writing music is as natural for the composer as eating or sleeping for all. Music is something that the composer happens to have been born for.

The composer, therefore, does not say to himself: “Do I feel inspired?” He says to himself: “Do I feel like working today?” And if he feels like working, he does. It is more or less like saying to himself: “Do I feel sleepy?” If you feel sleepy, you go to sleep. If you don’t feel sleepy, you stay up. If the composer doesn’t feel like working, he doesn’t work. It’s as simple as that.

小题1:What would be the best title for the text?

A.Composer: a man of mystery

B.Practice makes good music

C.Relation between sleeping and music

D.Music: product of nature小题2:Most people seem to think that a composer ____.

A.finds it difficult to write music

B.considers it important to have a good rest

C.should like to talk about inspiration

D.never asks himself very simple questions小题3:The author will most probably agree that composers ____.

A.are born with a gift for music

B.are people full of mystery

C.work late at night for their music

D.know a lot about eating and sleeping

单项选择题