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一、不同视角下的双曲线定义对于双曲线来说,依据不同视角可以得到多种形异质同的定义:(1)从立几视角:对顶圆锥被一个不经过圆锥顶点的平面所截,若平面与圆锥底面不平行,且与两部分圆锥都相交,则截得的曲线为双曲线,我们称之为双曲线的原始(最初)定义.当改变截面与圆锥底面的角度,亦可得到椭圆、抛物线以及圆.正因为都与圆锥相关,因此人们将之称为圆锥曲线,这正是人们将双曲线视为圆锥曲线的缘由.
First, the definition of hyperbola from different perspectives For hyperbolas, according to different perspectives can be obtained with a variety of different forms of the same definition: (1) From several perspectives: the top cone is not through a cone vertex plane cut , If the plane is not parallel to the bottom of the cone and intersects with both cones, the curve obtained is a hyperbola, which we call the original (initial) definition of the hyperbola. When changing the angle between the cross section and the bottom of the cone, Obtaining ellipses, parabolas, and circles Because of their conical correlation, people call it a conic, which is why people think of hyperbolic curves as conic curves.