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关于函数图象的伸缩变换,在讲解三角函数内容时多有涉及,本文借助椭圆与圆之间的伸缩关系,以一个全新的角度解决椭圆的弦长问题.图1例1在圆x2+y2=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?分析如图1,点P在圆x2+y2=4上运动,点P的运动引起点M的运动.我们可以由M为线段PD的中点得到点M与点P坐标之间的关系式,并由点P的坐标满足圆的方程得到点
Concerning the expansion and contraction transform of the function image, it is involved in explaining the content of the trigonometric function. In this paper, the problem of the chord length of the ellipse is solved with the help of the telescopic relationship between the ellipse and the circle. = 4 Take a point P, P point P for the vertical axis of the x-axis PD, D foot drop when the point P in the circle when the line segment PD of the mid-point M trajectory is what? Why? Analysis shown in Figure 1, The point P moves on the circle x2 + y2 = 4, the movement of the point P causes the movement of the point M. We can get the relation between the point M and the point P coordinates by M as the midpoint of the line segment PD, The coordinates satisfy the equation of the circle to get the point