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解析几何的基本观点,就是用一对有序实数来刻划一个点,用一个方程来描述一个点的集合—直线或曲线,从而实现了数与形的联系。于是,曲线性质的研究就可以通过对它的方程的性质的研究来完成。灵活应用方程的性质,就可以使许多解析几何问题简捷顺利的得到解决。方程的根与系数关系的应用,仅是一个方面,已有很多文章论及,本文举例说明方程的同解性在解析几何中的应用。
The basic idea of analytical geometry is to use a pair of ordered real numbers to delineate a point and use an equation to describe a set of points—a line or a curve—in order to achieve a connection between number and shape. Thus, the study of the nature of the curve can be accomplished by studying the properties of its equations. The flexible use of the properties of the equations allows many analytical geometric problems to be solved simply and smoothly. The application of the relationship between the root and the coefficient of the equation is only one aspect. Many articles have been discussed. This paper illustrates the application of the equivalence of the equation in analytic geometry.