AB是抛物线y的平方=2px的焦点弦,且|AB|=m;O为抛物线的顶点,则三角形AOB的面积是

设直线AB为：x=ky+p/2原点到AB的距离h=p/[2√(1+k^2)]把直线代入抛物线整理：y^2-2kpy-p^2=0于是：y1+y2=2kp,y1y2=-p^2m^2=(x1-x2)^2+(y1-y2)^2=(1+k^2)(x1-x2)^2=(1+k^2)(4k^2p^2+4p^2)=4p^2(1+k^2)√(1+k^2)=√[m^...