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人教版B版《数学》(选修2—1)P.39:平面内与两个定点F_1、F_2的距离的和等于常数(大于|F_1F_2|)的点的轨迹(或集合)叫做椭圆。看似简单的一句话,在教学过程中却常会出现一些理解上的误区,下面笔者结合例题进行说明。1误区分析例l已知半圆x~2+y~2=4(y≥0),动圆与此半圆相切且与z轴相切。求动圆圆心的轨迹方程。分析:设动圆圆心M的坐标为M(x,y),且过圆心作x轴的垂线MN,垂足为N,当两圆外切时,根据两圆外切时两圆心的距离等于两半径的和,可得|MO|=|MN|+2,利用两点间的距离公式,化简可
PEP B version of “Mathematics” (Electives 2-1) P.39: The trajectory (or set) of the point where the sum of the distances between a plane and two fixed points F_1 and F_2 equals a constant (greater than |F_1F_2|) is called an ellipse. In a seemingly simple sentence, there are often some misunderstandings in the process of teaching. The following examples illustrate the case with the author. 1 Misunderstanding analysis example 1 It is known that the semicircle x~2+y~2=4 (y≥0), the moving circle is tangential to the semicircle and tangent to the z-axis. The trajectory equation of the center of circle for seeking action. Analysis: Set the coordinates of the circle center M to be M (x, y), and the centerline of the circle centered on the x-axis is MN, and the foot is N. When the two circles are circumscribed, the distance between the two centers when the two circles are cut Equal to the sum of the two radii, available |MO|=|MN|+2, using the distance formula between the two points, simplifying