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对于反比例函数y=k/x(k≠0),有一个非常简单的性质,自变量与因变量的乘积等于比例系数k,即xy=k.有不少与反比例函数有关的数学竞赛题,利用这一简单的性质,就能获得巧妙的解答,下面仅举几例说明.例1(1992年全国初中数学竞赛试题)如图1,正比例函数y=kx和y=ax(a>0)的图象与反比例函数y=k/x(k>0)的图象分别交于A点和C点,若Rt△AOB和Rt△COD的面积分别为S_1和S_2,则S_1与S_2的关系是
For the inverse function y = k / x (k ≠ 0), there is a very simple property, the product of the independent variable and the dependent variable is equal to the proportional coefficient k, that is xy = k. There are many math competition questions related to the inverse proportion function, Example 1 (1992 National Junior High School Mathematical Contest Test Question) As shown in Figure 1, the proportional function y = kx and y = ax (a> 0) can be obtained by using this simple property, And the inverse proportion function y = k / x (k> 0) are respectively intersected with point A and point C. If the areas of Rt △ AOB and Rt △ COD are S_1 and S_2, respectively, the relationship between S_1 and S_2 Yes