过点P（2,1）的直线与抛物线y^2=16x交于A,B两点,且向量PA+向量PB=0,则此直线的方程为?

过点P（2,1）的直线与抛物线y^2=16x交于A,B两点,且向量PA+向量PB=0,则此直线的方程为?
过点P（2,1）的直线与抛物线y^2=16x交于A,B两点,且向量PA+向量PB=0,则此直线的方程为?

过点P（2,1）的直线与抛物线y^2=16x交于A,B两点,且向量PA+向量PB=0,则此直线的方程为?
let P（2,1）的直线 L:
(y-1)/(x-2) =m
y-1 = m(x-2)
x = (y-1+2m)/m
let A(x1,x2), B(x2,y2)
PA+PB =0
(x1-2,y1-1) +(x2-2,y2-1)=0
=(x1+x2-4, y1+y2-2) =0
=> x1+x2=4 and y1+y2=2
抛物线
y^2=16x
y^2= 16(y-1+2m)/m
my^2-16y-16(-1+2m) =0
y1+y2 = 16/m = 2
=> m = 8
L: (y-1)/(x-2) =8