与圆的直径相仿,经过有心圆锥曲线中心的弦叫做圆锥曲线直径,经研究,它有如下一个有趣的统一性质:定理AB是经过圆锥曲线x2m+y2n=1(mn≠0,m,n不同时为负)中心的弦,P是圆锥曲线上异于A,B外的任意一点,PA,PB的斜率分别为k1,k2,则k1k2=-nm(当m=n>0时,圆锥曲线是圆;当m>0,n>0,m≠n时,圆锥曲线是椭圆;当m和n异号时,圆锥曲线是双曲线). Similar to the diameter of a circle, the chord passing through the center of a conical curve of concentricity is called the diameter of a conic. It is interesting to note that the theorem AB follows the conic x2m + y2n = 1 (mn ≠ 0, m, n P is the point on the conic curve that is different from A, B, and the slopes of PA and PB are respectively k1 and k2, then k1k2 = -nm (when m = n> 0, the conic curve Is a circle; when m> 0, n> 0, m ≠ n, the conic is elliptical; when m and n are different, the conic is hyperbola).