问题 填空题

若点A的坐标为(3,2),F为抛物线y2=2x的焦点,点P在该抛物线上移动,为使得PA+PF取得最小值,则P点的坐标为______.

答案

由P向准线x=-

1
2
作垂线,垂足为M,由抛物线的定义,PF=PM,再由定点A向准线作垂线,垂足为N,那么点P在该抛物线上移动时,有PA+PF=PA+PM≥AN,当且仅当A,P,N三点共线时取得最小值AN=3-(-
1
2
)=
7
2
,此时P的纵坐标为2,继而求得横坐标为2.

故答案为:(2,2).

单项选择题

Modern liberal opinion is sensitive to problems of restriction of freedom and abuse of power. (1) , many hold that a man can be injured only by violating his will, but this view is much too (2) . It fails to (3) the great dangers we shall face in the (4) of biomedical technology that stems from an excess of freedom, from the unrestrained (5) of will. In my view, our greatest problems will be voluntary self-degradation, or willing dehumanization, as is the unintended yet often inescapable consequence of sternly and successfully pursuing our humanization (6) .

Certain (7) and perfected medical technologies have already had some dehumanizing consequences. Improved methods of resuscitation have made (8) heroic effort to "save" the severely ill and injured. Yet these efforts are sometimes only partly successful: They may succeed in (9) individuals, but these individuals may have sever brain damage and be capable of only a less-than-human, vegetating (10) . Such patients have been (11) a death with dignity. Families are forced to bear the burden of a (12) "death watch".

(13) the ordinary methods of treating disease and prolonging life have changed the (14) in which men die. Fewer and fewer people die in the familiar surroundings of home or in the (15) of family and friends. This loneliness, (16) , is not confined to the dying patient in the hospital bed. As a group, the elderly are the most alienated members of our society: Not yet (17) the world of the dead, not deemed fit for the world of the living, they are shunted (18) . We have learned how to increase their years, (19) we have not learned how to help them enjoy their days. Yet we continue to bravely and feverishly push back the frontiers (20) death.

13()

A.Even

B.But

C.Only

D.Hence

选择题