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平面解析几何是用代数的方法研究平面图形性质的一门学科。解题的基本方法是“坐标法”(或称“解析法”)。解题的一般步骤为:几何问题(翻译)代数问题(代数方法)代数结论(翻译)几何答案。要提高学生的解题能力,首先必须使学生明了解题的基本方法和一般步骤,善于进行几何语言与代数语言之间的“翻译”。同时还需注意以下几点。一、要重视定义、概念在解题中的应用。二次曲线的各种定义反映了自身最本质的属性,是理解这些曲线的概念,推导曲线的方程和解决有关问题的根本依据。解题中重视定义和概念的应用,有时能简化解题过程,利于提高学生的解题能力。
Plane analytic geometry is a discipline that uses algebraic methods to study the properties of planar graphics. The basic solution to the problem is the “coordinate method” (or “analytical method”). The general steps for problem solving are: Geometry Problem (Translation) Algebra Problem (Algebra Method) Algebra Conclusion (Translation) Geometry Answers. To improve the students' ability to solve problems, we must first make the students understand the basic methods and general steps, and be good at “translation” between geometric languages and algebraic languages. At the same time also pay attention to the following points. First, we must pay attention to the definition, the concept of problem solving in the application. The various definitions of conics reflect their most essential attributes, which are the concepts of understanding the curves, deriving the equations of the curves and the fundamental basis for solving the problems. Emphasis on problem solving and definition of the concept of application, sometimes to simplify the process of solving problems, which will help improve students' ability to solve problems.