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对称问题的一般解法往往从图形局部进行分解转化.但若从图形整体考虑,则能另僻新蹊,拓宽解题视野. 例1 给定椭圆C:x2+y2/4=1,过点M(1/2,1)能否作直线l,使l与给定椭圆C交于两点A、B,且M是线段AB的中点? 分析:若直线l存在,则A、B关于M对称.显然M不是椭圆C的对称中心,故A、B是椭圆C与其关于M对称的椭圆C’的公共点.
The general solution of the symmetry problem is often decomposed and transformed from the local part of the graph. However, if we consider it from the whole figure, we can find new ideas and broaden the horizon of problem solving. Example 1 Given an ellipse C: x2+y2/4=1, over the point M Is (1/2, 1) able to make a straight line l so that l intersects a given ellipse C at two points A, B, and M is the midpoint of the line segment AB? Analysis: If the line l exists, then A, B about M Symmetry. Obviously M is not the center of symmetry of the ellipse C, so A, B is the common point of the ellipse C and its ellipse C’ symmetrical about M.