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解析几何中的参数是个活泼的元素,在轨迹方程的探索中,活用参数,先求参数方程再化为普通方程的解题技巧早为大家熟知。其中参数的选择是问题的要害。本文仅举两例。介绍比值参数的应用。例1 设过原点与x轴正方向夹角为定值θ(锐角)的射线ON,x轴正向上有动点P,P与ON上的动点Q组成的△OPQ的面积为8。求PQ中点R的轨迹方程(下图1)。解:依题意,用三角形面积公式,有
The parameters in analytic geometry are active elements. In the exploration of trajectory equations, the use of parameters, and the solution of the equations of equations to normal equations are well known. The choice of parameters is the key to the problem. This article only gives two examples. Introduce the application of the ratio parameter. Example 1 Let ray ON be the angle between the origin and the positive direction of the x-axis as the fixed value θ (acute angle), and move the point P in the positive direction of the x-axis. The area of the △OPQ formed by the moving point Q on P and ON is 8. Find the trajectory equation for the PQ midpoint R (Figure 1 below). Solution: According to the meaning of the problem, use the triangle area formula,