Question

设过抛物线y2=4x的焦点F的直线交抛物线于A、B两点，且AB中点为M，则点M的轨迹方程是

我想知道把m点求出来以后怎样把k值消掉~~~

Answer 1

F(1,0)
M(x,y),yA+yB=2y
k(AB)=(yA-yB)=y/(x-1)
(yA)^2-(yB)^2=4(xA-xB)
(yA+yB)*(yA-yB)/(xA-xB)=4
2y*[y/(x-1)]=4
y^2=2(x-1)