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当一般二次曲线 ax~2+2bxy+cy~2+2dx+2ey+f=0 (1)为抛物型,且b≠0时,要确定它的位置、作出图形,是一个比较费事的问题。因为仅用不变量理论,却无法确定它的位置;而如用转轴、移轴公式,计算又较繁。本文试对这个问题,提供一个简便的方法。这一方法在理论的推导上,所用数学知识较少(用不着移、转轴公式,更用不着不变量理论);而在实际应用时,却是很简便的。
When the general quadratic curve ax~2+2bxy+cy~2+2dx+2ey+f=0 (1) is parabolic and b≠0, it is a more troublesome problem to determine its position and make a graph. . Because only the invariant theory is used, its position cannot be determined. If the axis and shift axis formulas are used, the calculation is more complicated. This article tries to provide a convenient method for this issue. This method is less theoretically used in the derivation of the theory (without moving, rotating axis formula, not using invariant theory); but in practical applications, it is very simple.