过抛物线x方=-4y的焦点F作直线交抛物线于A（x1,y1）B(x2,y2)两点,若y1+y2=-5,求|AB|的值

x^2=-4y=-2py,p=2,故焦点坐标是(0,-1)设过焦点的直线方程是y=kx-1,即有x=(y+1)/k代入到抛物线方程中有(y+1)^2/k^2=-4yy^2+2y+1=-4k^2yy^2+(2+4k^2)y+1=0y1+y2=-(2+4k^2)=-5k^2=3/4y1y2=1(y1-y2)^2=(y1+y2)^2-4y1y2=2...