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求曲线方程是解析几何研究的重要课题。这里我们把求曲线方程问题分为两种类型:第Ⅰ类型,已知曲线上的点符合某种条件,求曲线轨迹方程;第Ⅱ类型:已知某种类型的曲线具有某些特征,求此曲线方程。下面以解法为线索分别加以探讨。第Ⅰ类型问题已知曲线上的点符合某种条件,求动点的轨迹方程,也就是曲线方程。我们必须依题设中的几何关系和点的运动规律,通过分析,找出引起动点运动的根源,然后确定制约动点的
Finding the curve equation is an important issue in analytical geometry. Here we divide the problem of solving the curve equation into two types: Type I, the point on the known curve meets certain conditions, and the curve trajectory equation is found; Type II: It is known that certain types of curves have certain characteristics. This curve equation. The following solutions are used as clues. The type I problem has a point on the known curve that meets certain conditions. The trajectory equation of the action point is also the curve equation. We must follow the geometric relationship between the questions and the laws of movement of the points, through analysis, find out the root cause of the movement of the moving point, and then determine the constraints of the moving point.