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在解析几何里,常遇到“求某动点的轨迹”、“某动点的轨迹是什么图形”一类题目,对这些题目如何作答才准确(不多不少)?为了说明这个问题,我觉得有必要引进“圆锥曲线的个体特征”的概念。 一 圆很多,两个圆全等,当且仅当它们的直径等长,我们把直径长叫做圆的个体特征。 椭圆很多,两个椭圆全等,当且仅当它们的长轴等长,短轴也等长,我们把长轴长、短轴长叫做椭圆的个体特征。
In analytic geometry, it is often encountered a class of questions such as “finding the trajectory of a certain moving point” and “what is the trajectory of a certain moving point”. How accurate is the answer to these questions? (No more, no less)? To illustrate this problem, I think it is necessary to introduce the concept of “individual characteristics of conic curves.” There are many circles and two circles are equal. If and only if their diameters are equal, we call the diameter long the individual characteristics of the circle. There are many ellipses and two elliptical congruences. If and only if their long axis is equal, and the minor axis is also equal, we call the long axis and short axis the individual characteristics of the ellipse.