过抛物线y^2=4x焦点做一条直线交抛物线于A(x1,y1)B（x2,y2）,若y1+y2=2根号2

焦点(1,0)直线y=k(x-1)x=(y+k)/ky^2=4xky^2=4(y+k)ky^2-4y-4k=0y1+y2=4/k=2根号2k=2/根号2=根号2y=根号2(x-1)2(x-1)^2=4xx^2-4x+1=0|AB| =根号(1+k^2)根号(x1+x2)^2-4x1x2=根号3*根号(16-4)=根号3*根号12=6...