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解析几何是数学中的一个重要分支。本文通过对教材和高考题目的分析阐述了如何抓住曲线的方程来研究其性质,如何利用“点在曲线上”与“坐标和方程组”的内在关系解题。解析几何是通过坐标系把点和坐标,曲线和方程联系起来的一个数学分支,它是数学中数形结合的典范。通过用方程来研究曲线的性质,从而达到用代数方法来研究几何问题的目的,这就是解析几何的神来之笔,既“神”;几何中的点与曲线的关系,是通过点的坐标与曲线的方程来体现的,从而“点在曲线上”就成了平面解析几何中最基本和最重要的表述,它是实现用代数方法来研究几何问题的一个基石,也就是平面解析几何的“形”。
Analytic geometry is an important branch of mathematics. This article explains how to grasp the equation of the curve to study its nature through the analysis of textbooks and college entrance examination questions. How to use the relationship between “points on the curve” and “coordinates and equations” to solve problems. Analytic geometry is a branch of mathematics that associates points with coordinates, curves, and equations through a coordinate system. It is a paradigm for the combination of numbers and shapes in mathematics. Through the use of equations to study the nature of the curve, so as to achieve the purpose of using algebraic methods to study geometric problems, which is the analytical writing of the gods, not only “God”; the relationship between points and curves in geometry, is through the point coordinates and curves The equation is embodied so that “points on the curve” becomes the most basic and most important representation of plane analytic geometry. It is a cornerstone for realizing the study of geometric problems using algebraic methods, that is, the “shape” of plane analytical geometry. .