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全日制普通高级中学教科书(必修)《数学》第二册(上)讲述了一般双曲线的性质,本文针对特殊的双曲线做进一步的探讨和研究.为行文方便,我们规定:离心率e=(5~(1/2)+1)/2的双曲线为优等双曲线,简称优双曲线.通过探究可以得出优双曲线的以下性质.性质1 双曲线是优双曲线的充要条件是以双曲线的实轴的一个端点及离它较远的焦点为直径的圆过双曲线的虚轴的端点.如图1所示,双曲线(x~2/a~2)-(y~2/b~2)=1的左顶点为 A,右焦点为 F,B 是虚轴的一个端点.
Full-time ordinary high school textbooks (compulsory) “Mathematics” Volume II (on) describes the general nature of the hyperbola, this paper for further study and study of hyperbola for convenience, we provide: eccentricity e = (5 ~ (1/2) +1) / 2 hyperbolic curve for the superior hyperbolic, referred to as the hyperbolic. By exploring the following hyperbolic can be drawn Properties. Properties 1 hyperbolic hyperbolic curve is necessary and sufficient conditions Is the end point of the imaginary axis of hyperbola passing through an end point of the hyperbola real axis and a circle whose diameter is farther from it. As shown in Figure 1, the hyperbola (x ~ 2 / a ~ 2) - (y ~ 2 / b ~ 2) = 1 The left vertex is A, the right focus is F, and B is an endpoint of the imaginary axis.