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运动与静止是对立统一的一个整体,两者之间经常处于一种互动的状态.解题中要辩证地对待运动与静止的关系,并根据条件适时进行互化.以下笔者谈一谈动静转换策略在解析几何中的应用. 一、化静为动,动态分析 “化静为动”实质上是化特殊为一般,将相对静止的数学问题找到相应的动态背景,有助于全面、深入地分析问题、解决问题.它具体表现为解析法、待定系数法、参数法等. 例1 求经过点P(7～(1/7),20/3),且渐近线为4x±3y=0的双曲线方程. 解:设双曲线方程为16x-9y2=λ(λ≠0),将点P坐标代入得λ=-288,故双曲线方程为y2/32-x2/18=1.
Movement and stillness are a unity of opposites and the two are often in an interactive state. The problem should be treated dialectically in relation to the relationship between motion and rest, and be interdependent in time according to the conditions. The following writer talks about motion and static transformation. The application of strategy in analytical geometry. First, the static and dynamic, dynamic analysis of “static to dynamic” is essentially the special as the general, the relatively static mathematical problem to find the corresponding dynamic background, is conducive to a comprehensive and in-depth Analyze the problem and solve the problem. It is specifically represented by analytical method, undetermined coefficient method, parametric method, etc. Example 1 Find the point P (7 ~ (1/7), 20/3), and the asymptote is 4x ± 3y = The hyperbolic equation of 0. Solution: Let the hyperbolic equation be 16x-9y2=λ(λ≠0), and substitute the point P coordinate into λ=-288, so the hyperbolic equation is y2/32-x2/18=1.