抛物线y^2=2px(p>0),设AB为焦点弦,O为抛物线的顶点,且AO的延长线交准线于C,求证BC平行于x轴.

p>0 AB为抛物线y^2=2px焦点F的弦,O为抛物线的顶点,且AO的延长线交准线于C,则 抛物线的准线x=-0.5p,焦点F(0.5p,0) 设A(2pa^2,2pa),B(2pb^2,2pb),则 k(AB)=(2pa-2pb)/(2pa^2-2pb^2)=1/(a+b) k(AF)=2pa/(2pa^2-0.5p)=4a...