轨迹这个概念由于它的严谨性和抽象性的确不易领会,尤其初学者不易接受,执教者亦不易讲深讲透。它是一种几何图形,具有必要性和充分性。当论证时二者是缺一不可的。所谓必要性也就是完备性或者无遗漏。对于综合几何而言即合于指定条件的流动点“必”在一个特定的图形上,也就是完全在那图形上,从而沒有遗漏任何合条件的点于那图形之外。对于解析几何而言即合于指定条件的任一流动点的坐标“必”适合于坐标的某数学关系式(此关系式一般为一方程有时则是一条件不等式或不等兼等式)。前者图形为曲线,后者则是以曲线为界线的平面区域。所谓充分性也就是纯粹性或无混杂。对于综合几何而言即只要某点在此图形上,则它“就”合于特定的条件,也就是此图形中毫无不合指定条件之点,亦即此图形是由合条件的一切点所构成,从而毫未混杂不合条件之点在内。对于解析几何而言则是只要某点坐标合于该数学关系式它“就”合于特定条件。点之坐标既 The concept of trajectory is difficult to grasp because of its rigor and abstractness, especially for beginners. It is not easy for instructors to speak up. It is a geometric figure with necessity and sufficiency. Both are indispensable when the argument is made. The so-called necessity is completeness or omission. For synthetic geometries, the flow point that fits into the specified condition “must” be on a specific pattern, that is, completely on that graph, so that no points that are fit to the condition are omitted from that graph. For analytic geometry, the coordinates of any floating point that fit into the specified conditions must be appropriate to the mathematical relationship of the coordinates (this relationship is generally an equation and sometimes a conditional inequality or inequality). The former is a curve, while the latter is a flat area with a curve as the boundary. The so-called adequacy is either pure or mixed. For an integrated geometry, that is, as long as a certain point is on the graph, it “fits” with a specific condition, that is, there is no point in the graph that does not meet the specified condition, that is, this graph is made up of all points of the condition. The composition, so as not to mix unsatisfactory points. For analytic geometry, as long as the coordinates of a certain point fit into the mathematical relation, it “fits” into certain conditions. Point coordinates are both