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椭圆是圆锥曲线的核心内容之一,椭圆的方程、几何性质等核心知识与圆有很多相似之处.最近,笔者遇到了一次学生的追问,引发了一场意外的探究,感触颇深.现整理出来,与同行们交流探讨.1问题再现人教A版选修2-1第41页例2及题后思考:题目如图1,在圆x~2+y~2=4上任取一点P,过点P作x轴的垂线段PD,D为垂足.当点P在圆上运动时,线段PD的中点M的轨迹是什么?为什么?
Ellipse is one of the core contents of the conic curve, the elliptical equation, geometric properties and other core knowledge has many similarities with the circle. Recently, I encountered a student’s questioning, triggering an unexpected exploration, deep feelings. Sorting out and discuss with their peers.1 The question of reproduction of human teach A version of elective 2-1 Page 41 Example 2 and thinking after the question: the title shown in Figure 1, in the circle x ~ 2 + y ~ 2 = 4 take a point P , The point P for the vertical axis of the x-axis PD, D foot drop when the point P in the circular motion, the line segment PD of the mid-point M of what is the track and why?