过抛物线y^2=2px(p>0)的焦点作互相垂直的两条弦,求以这两条弦为对角线的四边形面积的最小值
问题描述：
过抛物线y^2=2px(p>0)的焦点作互相垂直的两条弦,求以这两条弦为对角线的四边形面积的最小值
答
p>0F(0.5p,0)过F互相垂直的两条弦:AB⊥CDAB或CD⊥X轴,则不符合已知条件,故AB、CD不⊥X轴设AB:y=k(x-0.5p),x=(y+0.5pk)/ky^2=2px=2p*(y+0.5pk)/kky^2-2py-kp^2=0(yA+yB)=2p/k,yA*yB=-p^2(yA-yB)^2=(yA+yB)^2-4yA*yB=(...