黄海波老师在《数学通讯》“椭圆的一个性质”一文中给出了椭圆的一个与面积比有关的优美性质.笔者经过研究发现双曲线也有一个类似的美妙性质,具体阐述如下:定理3双曲线x2a2-y2b2=1(a>0,b>0),A(a,0),B(0,b),点M满足→BM=λ→MA(λ>1),直线OM交双曲线于C,D两点(其中O为坐标原点),△ABC与△ABD的面积分别记为S1, Huang Haibo gave a beautiful elliptic ellipsoid with area ratio in the article of “Mathematical Communication” “The Nature of Ellipses.” After studying, the author found that the hyperbola has a similar wonderful nature as follows: Theorem 3 The hyperbolas x2a2-y2b2 = 1 (a> 0, b> 0), A (a, 0) and B (0, b), and the point M satisfies → BM = λ → MA Curve in C, D two points (where O is the origin of coordinates), △ ABC and △ ABD area were recorded as S1,