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椭圆、抛物线、双曲线各有自己的标准方程,如果用它们来解决有关二次曲线的共性问题,那就必须通过“穷举”,实际上要解决三个问题,这显然是不方便的。二次曲线的统一极坐标方程,对于解决某些问题比较方便,但对另外一些问题,并不方便。如果把统一的极坐标方程p=ep/1-(ecosθ)化为直角坐标方程,则所得的方程较繁,应用起来也不方便。本文特提供一个简单的二次曲线的统一直角坐标方程,用它来解决某些二次曲线的共性问题,较为简捷。
Ellipses, parabolas, and hyperbolas each have their own standard equations. If they are used to solve common problems related to quadratic curves, they must pass “exhaustive” and actually have to solve three problems, which is obviously inconvenient. The uniform polar equation of the quadratic curve is convenient for solving certain problems, but it is not convenient for other problems. If the uniform polar coordinate equation p=ep/1-(ecosθ) is converted into a rectangular coordinate equation, the resulting equation is more complicated and inconvenient to apply. This article provides a simple quadratic curve of the uniform rectangular coordinate equation, use it to solve the common problem of some quadratic curves, it is more simple.