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?
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![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?](/uploads/image/z/7259489-17-9.jpg?t=%E8%BF%87%E7%82%B9P%EF%BC%882%2C1%EF%BC%89%E7%9A%84%E7%9B%B4%E7%BA%BF%E4%B8%8E%E6%8A%9B%E7%89%A9%E7%BA%BFy%5E2%3D16x%E4%BA%A4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E4%B8%94%E5%90%91%E9%87%8FPA%2B%E5%90%91%E9%87%8FPB%3D0%2C%E5%88%99%E6%AD%A4%E7%9B%B4%E7%BA%BF%E7%9A%84%E6%96%B9%E7%A8%8B%E4%B8%BA%3F)
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