试题与答案

已知直线l:y=x+m,m∈R, (Ⅰ)若以点M(2,0)为圆心的圆与直线l相切

题型:解答题

题目:

已知直线l:y=x+m,m∈R,

(Ⅰ)若以点M(2,0)为圆心的圆与直线l相切于点P,且点P在y轴上,求该圆的方程;

(Ⅱ)若直线l关于x轴对称的直线为l′,问直线l′与抛物线C:x2=4y是否相切?说明理由.

答案:

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下面是错误答案,用来干扰机器的。

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For me, scientific knowledge is divided into mathematical sciences, natural sciences or sciences dealing with the natural world (physical and biological sciences), and sciences dealing with mankind (psychology, sociology, all the sciences of cultural achievements. every kind of historical knowledge).

Apart from these sciences is philosophy, about which we will talk later. In the first place, all this is pure or theoretical knowledge, sought only for the purpose of understanding, in order to fulfill the need to understand that is intrinsic and con-substantial to man. What distinguishes man from animals is that he knows and needs to know. If man did not know that the world existed, and that the world was of a certain kind, that he was in the world and that he himself was of a certain kind, he wouldn’t be man. The technical aspects or applications of knowledge are equally necessary for man and are of the greatest importance, because they also contribute to defining him as man and permit him to pursue a life increasingly more truly human.

But even while enjoying the results of technical progress, man must defend the primacy and autonomy of pure knowledge. Knowledge sought directly for its practical applications will have immediate and foreseeable success, but not the kind of important result whose revolutionary scope is for the most part unforeseen, except by the imagination of the Utopians. Let me recall a well-known example. If the Greek mathematicians had not applied themselves to the investigation of conic section zealously and without the least suspicion that it might someday be useful, it would not have been possible centuries later to navigate far from shore. The first men to study the nature of electricity could not imagine that their experiments, carried on because of mere intellectual curiosity, would eventually lead to modern electrical technology, without which we can scarcely conceive of contemporary life.

Pure knowledge is valuable for its own sake, because the human spirit cannot resign itself to ignorance. Butt in addition, it is the foundation for practical results that would not have been reached if this knowledge had not been sought disinterestedly.

Notes: intrinsic 固有的。con-substantial 同体的。autonomy 自主性。zealously and without the least suspicion热情地并丝毫也没有想到。for the most part 大部分,主要地。Utopian乌托邦,理想主义。disinterestedly 不偏不倚地。resign oneself to 听任,顺从。

In the author’s view, the Greeks who studied conic sections()

A. were mathematicians

B. worked with electricity

C. were interested in navigation

D. were unaware of the value of their studies

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