Question

如图已知抛物线c1y=x^2-2x+4和直线ly=-2x+8,直线y=kx与抛物线c1交于两不同

Answer 1

把y=kx代入y=x^2-2x+4得x^2-(k+2)+4=0,

设A(x1,y1),B(x2,y2),则x1+x2=k+2,x1x2=4,

把y=kx代入y=-2x+8得(k+2)x=8,xP=8/(k+2),

原点O在直线y=kx上,

∴OP/OA+OP/OB=xP/x1+xP/x2=xP(x1+x2)/(x1x2)

=8/(k+2)*(k+2)/4=2,

∴1/OA+1/OB=2/OP.