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我们通常通过“数形结合”的方法判断过定点的直线与双曲线x2/a2-y2/b2=1能否相切,强调对图形的感知能力。本文拟用严格的代数方法说明定点与双曲线的位置关系对切线条数及切点位置的影响。
We usually judge whether the line between the fixed point and the hyperbole x2/a2-y2/b2=1 can be tangent by the method of “number combination”, and emphasize the perception ability of the figure. This paper intends to use strict algebraic methods to explain the positional relationship between fixed point and hyperbola and the effect of the number of cut lines and the position of the cut point.