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解析几何是用代数方法来研究几何问题的一门数学学科,因而如何减少计算量,培养学生的求简意识便成为解析几何的一个十分实出的问题,下面结合教材谈谈个人在教学中的体会。一、求简意识是建立在对概念深入理解的基础之上的只有深入理解概念的本质,才能恰当灵活地应用概念简化解题过程。例1 通过双曲线x~2/144-y~2/25=1的一个焦点作x轴的垂线,求垂线和双曲线的交点与两焦点的距离(课本第102面第11题)。多数同学先求焦点及交点坐标再求距离。我问学生:能否用双曲线定义来解呢?为什么?学生答:能;因为此题涉及双曲线上一点到两焦点的距
Analytic geometry is a mathematics discipline that uses algebraic methods to study geometric problems. Therefore, how to reduce the amount of calculations and cultivate students’ sense of conciseness has become a very real problem in analytical geometry. The following combination of teaching materials to talk about personal teaching Experience. First, the Simplification Consciousness is based on a deep understanding of the concept. Only by understanding the essence of the concept in depth, can the concept be used properly and flexibly to simplify the problem-solving process. Example 1 Use the vertical line of the x-axis as a focal point of the hyperbola x~2/144-y~2/25=1 to find the distance between the intersection point of the perpendicular line and the hyperbola and the two focal points (Textbook No.102, Item 11). . Most students first seek the focal point and the coordinates of the intersection to find the distance again. I asked students: Can we use the hyperbolic definition to solve it? Why? Student A: Yes; because this question involves the distance from one point to two focal points on the hyperbola