F(p/2,0),設(shè)AB直線方程為：y=k(x-p/2),代入拋物線方程,k^2*(x-p/2)^2=2px,k^2*x^2-p(k^2+1)x+p^2/4=0,
解得：x1=[p(k^2+1)+2p√(k^2+1)]/(2k^2),
x2=[p(k^2+1)-2p√(k^2+1)]/(2k^2),
再代入直線方程求得：y1=p(1+√(k^2+1))/k, y2=p(1-√(k^2+1))/k
即A(x1,y1),B(x2,y2)
設(shè)M(-p/2,y3),則MF的斜率kmf=-y3/p,
MA的斜率kma=(y3-y1)/(-p/2-x1)=(kp(1+√(k^2+1)-k^2*y3)/[p(k^2+1+√(k^2+1))],
MB的斜率kmb=(y3-y2)/(-p/2-x2)= (kp(1-√(k^2+1)-k^2*y3)/[p(k^2+1-√(k^2+1))],
kma+kmb=-2*y3/p=2*kmf,
所以,MA,MF,MB斜率成等差數(shù)列