已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a＋u=

已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a＋u=
已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a＋u=

已知抛物线y²=2px(p>0).过点E(m,0).(m不等于0)的直线交抛物线于点M,N,交y轴于点P,向量PM等于a向量ME,向量PN=u向量NE,则a＋u=
设MN:x=ky+m,①交y轴于P(0,-m/k),
把①代入y^2=2px,得y^2-2kpy-2mp=0,
设M(x1,y1),N(x2,y2),则y1+y2=2kp,y1y2=-2mp,
由向量PM=a向量ME,得(x1,y1+m/k)=a(m-x1,-y1),②
由向量PN=u向量NE,得(x2,y2+m/k)=u(m-x2,-y2),③
由②,y1+m/k=-ay1,
由③,y2+m/k=-uy2,
∴a+u=-2-(m/k)(1/y1+1/y2)=-2-(m/k)(y1+y2)/(y1y2)
=-2-(m/k)(2kp)/(-2mp)=-1.