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问题 解答题
已知动点P到直线x=-1的距离与到定点C(
1
2
，  0)的距离的差为
1
2
．动点P的轨迹设为曲线C．
（Ⅰ）求曲线C的方程；
（Ⅱ）设过点A（-4，0）的直线与曲线C交于E、F两点，定点A'（4，0），求直线A'E、A'F的斜率之和．
答案

（Ⅰ）由题意知，动点P到定点C(

1
2
，  0)的距离等于到定直线x=-
1
2
的距离，

所以动点P的轨迹为抛物线，

且

p
2
=
1
2
，

P=1．

所以点P的轨迹方程为y2=2x．…（6分）

（Ⅱ）设过点A的直线方程为y=k（x+4）（k≠0）．

联立方程组

y=k(x+4)
y2=2x
，

消去x，得

k
2
y2-y+4k=0．…（8分）

设E（x1，y1）、F（x2，y2），

则y1•y2=8，且y12=2x1，y22=2x2．

∵kA′E=

y1
x1-4
，kA′F=
y2
x2-4
，

∴kA′E+kA′F=

y1
x1-4
+
y2
x2-4
=
y1x2-4y1+y2x1-4y2
(x1-4)(x2-4)

=

y1
y22
2
-4y1+y2
y21
2
-4y2
(x1-4)(x2-4)

=

(y1+y2)(
y1
y 2
2
-4)
(x1-4)(x2-4)
．

由y1•y2=8，得kA'E+kA'F=0．…（14分）

问答题 简答题

在保证焊接质量的情况下，如何减小焊接热影响区？
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单项选择题

Cooperation is the common endeavor of two or more people to perform a task or reach a jointly cherished goal. Like competition and conflict, there are different forms of cooperation, based on group organization and attitudes.
In the first form, known as primary cooperation, group and individual unite. The group contains nearly all of each individual’s life. The rewards of the group’s work are shared with each member. There is an interlocking identity of individual, group, and task performed. Means and goals become one, for cooperation itself is valued.
While primary cooperation is most often characteristic of preliterate societies, secondary cooperation is characteristic of many modem societies. In secondary cooperation, individuals devote only part of their lives to the group. Cooperation itself is not a value. Most members of the group feel loyalty, but the welfare of the group is not the first consideration. Members perform tasks so that they can separately enjoy the fruits of their cooperation in the form of salary, prestige, or power. Business offices and professional athletic teams are examples of secondary cooperation.
In the third type, called tertiary cooperation or accommodation, latent conflict underlies the shared work. The attitudes of the cooperating parties are purely opportunistic; the organization is loose and fragile. Accommodation involves common means to achieve antagonistic goals; it breaks down when the common means cease to aid each party in reaching its goals. This is not, strictly speaking, cooperation at all, and hence the somewhat contradictory term antagonistic cooperation is sometimes used for this relationship.

Which of the following statements about primary cooperation is supported by information in the passage

A．It was limited in prehistoric times.

B．It is usually the first stage of cooperation achieved by a group of individuals attempting to cooperate.

C．It is an ideal that can never be achieved.

D．It is most commonly seen among people who have not yet developed reading and writing skills.
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