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现行重点中学课本《解析几何》第81页15题:“一条县段AB(AB=2a)的两端点A和B分别在x轴和y轴上滑动。求线段AB的中点M的轨迹方程”。我们以它为例说明如何对习题多解、引伸和联想。一、多解。对习题的条件和结论从不同角度去思考,探求各种不同的解法,是培养学生解题能力的一个重要方法。 1、直接法:设M(x,y),则M点的集合P={M||OM|=a},∴(x~2+y~2)~(1/2)=a,所求轨迹方程为x~2+y~2=a~2。 2、转移法:设M(x,y),则A(2x,0),B(0,2y),∴((2x)~2+(2y)~2)~(1/2)=(2a)~2,故轨
The current key middle school textbook “Analytic Geometry”, page 81, 15 questions: “A county AB (AB = 2a) at both ends of the point A and B are sliding on the x-axis and y-axis. Find the midpoint of the AB segment M of the trajectory equation ”. We use it as an example to explain how to solve, extend, and associate problems. One, many solutions. Thinking about the conditions and conclusions of the exercises from different perspectives and exploring various solutions is an important way to cultivate students’ ability to solve problems. 1. Direct method: Let M(x,y) be a set of M points P={M||OM|=a}, ∴(x~2+y~2)~(1/2)=a, The trajectory equation is x~2+y~2=a~2. 2. Transfer method: Let M(x,y), then A(2x,0), B(0,2y), ∴((2x)~2+(2y)~2)~(1/2)=( 2a)~2, track