论文部分内容阅读
在直角坐标系中,椭圆、双曲线、抛物线各有自己的标准方程,用这些标准方程去研究圆锥曲线的共性,一般地说是比较麻烦的.在极坐标系中,根据圆锥曲线的统一定义,得到了它的统一方程ρ=(ep)/(1-ecosθ)(e>0).这个统一方程对研究圆锥曲线的共性提供了简捷的方法,在解几的综合复习中,补充圆锥曲线统一方程的应用,对提高学生处理二次曲线的解题能力,是十分有效的.现从五个方面举例谈谈它的应用,供师生们参考.
In Cartesian coordinates, ellipses, hyperbolas, and parabolas each have their own standard equations. Using these standard equations to study the commonality of conic curves is generally more troublesome. In polar coordinates, the uniform definition of conic curves is used. The uniform equation ρ=(ep)/(1-ecosθ)(e>0) is obtained. This unified equation provides a simple method for studying the commonality of conic curves. In the comprehensive review of several solutions, the conical curve is supplemented. The application of the unified equation is very effective in improving the ability of students to solve quadratic curve problem solving. Now we will discuss its application from five aspects for reference by teachers and students.