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一条曲(直)线经过适当的变化后,得到另一条与它有关的曲(直)线,叫做曲(直)线的初等变换.曲(直)线的初等变换包括平移、对称、伸缩三种变换.高考中经常出现有关曲(直)线的初等变换的考题,而现行的高中教材没有对曲(直)线的初等变换作系统的阐述,因此考生在解这类题时,失分严重.下面就有关曲(直)线的初等变换以定理(证明略)的形式作详细的叙述,供参考.一、曲线的平移变换定理1 曲(直)线 F(x,y)=0向左平行移动a(a>0)个单位长度,得到曲(直)线 F(x+a,y)=0;向右平行移动 a(a>0)个单位长度,得到曲(直)线
After a line (straight line) has been properly changed, another line related to it is obtained, which is called the elementary transformation of the line (straight line). The elementary transformations of the line (straight line) include translation, symmetry, and telescoping. In the college entrance examination, there are often questions about the elementary transformation of the music (straight line), and the current high school textbooks do not systematically describe the elementary transformation of the music (straight line), so the candidates lose points in solving such questions. Seriously. The following is a detailed description of the elementary transformation of the straight line (the proof) in the form of a theorem (protocol omitted) for reference. A. The translation transformation of the curve Theorem 1 The straight line F(x,y)=0 Move a (a>0) units of length to the left in parallel to obtain a curved (straight) line F(x+a,y)=0; move a (a>0) unit length to the right to obtain a straight (straight) line