笔者对双曲线渐近线上的点作了一些研究,得到了几个有趣的最大值点,现说明如下,供读者学习参考.定理P是双曲线x~2/a~2-y~2/b~2=1(a>0,b>0)渐近线上的一点,F是双曲线焦点,A是与F相应的顶点,E是与F相应的准线与x轴的交点,P与A,E,F均位于y轴的同一侧,e是双曲线离心率, The author made some research on hyperbolic asymptotic points, and got some interesting maxima, as follows, for the reader to learn the reference. Theorem P is hyperbolic x ~ 2 / a ~ 2-y ~ 2 / b ~ 2 = 1 (a> 0, b> 0), F is the hyperbolic focus, A is the vertex corresponding to F, E is the intersection of the quasi-line corresponding to F and the x axis, P and A, E, F are located on the same side of the y-axis, e is hyperbolic eccentricity,