本文拟讨论由坐标平面内任意点P（x。，yo），引双曲线C1：的切线，切线的存在性、切线的条数、切线方程及切点坐标．不妨只考察P在原点、P在坐标药正半轴上、P在第一象限内的情形．如图所示，记C1的渐近线为＝0，C1的右顶点为A（a，O），直线C3：x＝alC3与C2的交点为B（a，b） This paper discusses the tangent line, the existence of the tangent line, the number of tangent lines, the tangent equation and the tangent point coordinate of the hyperbolic line C1: from any point P(x., yo) in the coordinate plane. We may consider only the case where P is at the origin, P is on the positive half of the coordinates, and P is in the first quadrant. As shown in the figure, the asymptotes of C1 are = 0, the right vertex of C1 is A(a, O), and the line C3:x = the intersection of alC3 and C2 is B(a,b)