在圆锥曲线中,蕴涵着许多结构新颖独特、内容丰富多彩的性质,我在学习过程中发现,双曲线中有几个有趣的定值,介绍如下.性质1过双曲线x~2/a~2-y~2/b~2=1(a>0,b>0)上任意一点P作双曲线的两条渐近线的平行线,分别交另一条渐近线于点M,N,则PM·PN=a~2+b~2/4.证明设点P(x_0,y_0),记过点P且与双曲线的渐近线平行的直线为l_1,l_2.因为双曲线的渐近线的方程为y=±b/ax,所 In the conic, contains many novel and unique structure, rich and colorful nature, I found in the learning process, there are several interesting hyperbolic values, described below. Nature 1 Hyperbolic x ~ 2 / a ~ 2-y ~ 2 / b ~ 2 = 1 (a> 0, b> 0) at any point P for the hyperbolic two parallel lines of asymptotes, respectively, to pay another asymptote at points M, N, Then PM · PN = a ~ 2 + b ~ 2 / 4. Prove that the point P (x_0, y_0), point P and with the asymptotic curve of the hyperbola parallel lines l_1, l_2 because hyperbolic asymptotic The equation of the line is y = ± b / ax