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文[1]从一道课本习题出发,通过探究,得到一系列结论,并最终统一为:过二次曲线Ax2+Cy2+Dx+Ey+F=0(A2+C2≠0)上一点P(x0,y0)的两条直线与曲线交于A、B两点,满足kPA·kPB=t(t≠0),则直线AB过定点(坐标略).笔者读后发现,由于作者的疏忽,文中的推广结论4的证明存在瑕疵,以致结论4、5、6、7存在缺陷,需要修正.同时,笔者对各结论进行了逆向探究,均得到相应结论.
Starting from a textbook exercise, we get a series of conclusions through exploration, and finally conclude that the quadratic curve is: Quadratic curve Ax2 + Cy2 + Dx + Ey + F = 0 (A2 + C2 ≠ 0) Previous point P , y0) of the two lines and the intersection of the curve and the intersection of A and B two points, satisfy kPA · kPB = t (t ≠ 0), then the line AB over a fixed point (coordinates omitted.) I read that due to the author’s negligence, Of the conclusions of the conclusion 4 of the existence of flaws, so conclusions 4, 5, 6, 7 flaw, need to be amended at the same time, the author of the conclusions of the reverse exploration, are the corresponding conclusions.