(1)设A(x1,y1),B(x2,y2),则有x1y1=x2y2=1, ∵S△ODB=×BD×OD=x2y2=,S△OCA=×OC×AC=x1y1=,故①正确;
(2)由已知,得P(x1,y2), ∵P点在y=的图象上, ∴S矩形OCPD=OC×PD=x1y2=k, ∴S四边形PAOB=S矩形OCPD-S△ODB-S△OCA=k--=k-1,故②正确;
(3)由已知得x1y2=k,即x1•=k, ∴x1=kx2, 根据题意,得PA=y2-y1=-=,PB=x1-x2,=(k-1)x2,故③错误;
(4)当点A是PC的中点时,y2=2y1, 代入x1y2=k中,得2x1y1=k, ∴k=2, 代入x1=kx2中,得x1=2x2,故④正确.
故本题答案为:①②④. |