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研究动点的轨迹方程是平面解析几何的基本问题之一。在复习课中,系统地总结归纳求轨迹方程的规律和基本方法,对学生理解和掌握这个内容是十分重要的。下面谈些不成熟的看法,供同行参考。一、通过对比,抓住本质,揭示规律。在平面解析几何中,曲线方程又称轨迹方程。学生在最初学习这个概念时,由于只有函数图象的基础,没有圆锥曲线的概念,感性知识并不丰富,尔后学习圆锥曲线时,又把主要精力放在掌握圆锥曲线的性质上,因此,学生对轨迹方程的求法,往往抓不住要领。针对这种情况,我在复习中,引导学生把求轨迹方程与代数中列方程、函数中求函数表达式联系起来,分别举例,对比分析,让学生明确以下两点: 1.在代数中,列一元方程解应用题,设一个未知数,列得一元方程,f(x)=0,一般来说,它的解是确定的。求函数表达式,要设出自变数x和因变数y,列出显式y=f(x),一般有无数组对应值,把每组对应值作为一点的坐标,就形成函数的图象。而求轨迹方程,在给定的坐标系下,要设出动点坐标(x,y)或(ρ,θ),
The trajectory equation of the study point is one of the basic problems of plane analytical geometry. In the review class, systematically summarizing the laws and basic methods of trajectory equations is very important for students to understand and master this content. Let’s talk about some immature ideas for reference by peers. First, through comparison, grasp the essence and reveal the law. In plane analytic geometry, the curve equation is also called the trajectory equation. When students first learned this concept, they had no concept of conic curve because of only the basis of the function image. Perceptual knowledge was not abundant. After learning conic curves, they focused on grasping the nature of conic curves. Therefore, students The method of trajectory equation is often unable to grasp the essentials. In view of this situation, in the review, I guide students to relate the trajectory equations to the expressions in the algebraic equations and function expressions in the functions. For example, comparative analysis allows the students to specify the following two points: 1. In algebra, The equations for solving one-dimensional equations are solved by applying an unknown number and a one-dimensional equation, f(x)=0. Generally speaking, its solution is definite. To find the function expression, set the variable x and the variable y, and list the explicit y=f(x). Generally there is no corresponding value of the array. The corresponding value of each group is used as the coordinate of one point to form the image of the function. To find the trajectory equation, in the given coordinate system, we must set the moving point coordinates (x, y) or (ρ, θ),