解析几何不仅仅是运用代数的方法研究几何,更是“数”与“形”的统一、代数与几何的结合。椭圆、双曲线、抛物线各自的定义反映了它们各自的几何特征,不少涉及到与焦点有关的问题,若能灵活运用曲线的定义、性质等知识,往往能简化解题过程,提高解题速度,现举例说明圆锥曲线的定义在解竞赛题中的应用,供同学们参考。 Analytic geometry is not only the use of algebraic methods to study geometry, but also the unification of “numbers” and “shapes” and the combination of algebra and geometry. The definitions of ellipse, hyperbola, and parabola reflect their respective geometric characteristics. Many involve problems related to focus. If knowledge about the definition, nature, etc. of the curve can be flexibly used, the problem-solving process can be simplified and the problem-solving speed can be improved. This is an example of the application of the definition of the conic section in solving competition questions for students’ reference.