1.如圖,點(diǎn)A(a,0),B(0,b),滿足(a-1)
2+|2-2b|=0,若點(diǎn)P為射線OA上異于原點(diǎn)O和點(diǎn)A的一個(gè)動(dòng)點(diǎn).(1)如圖1,
①直接寫(xiě)出點(diǎn)A的坐標(biāo)為
,點(diǎn)B的坐標(biāo)為
;
②當(dāng)點(diǎn)P位于點(diǎn)O與點(diǎn)A之間時(shí),連接PB,以線段PB為邊作等腰直角△BPE(P為直角頂點(diǎn),B,P,E按逆時(shí)針?lè)较蚺帕校B接AE.求證:AB⊥AE;
(2)點(diǎn)D是直線AB上異于點(diǎn)A與點(diǎn)B的一點(diǎn),使得∠BPO=∠APD,過(guò)點(diǎn)D作DF⊥BP交y軸于點(diǎn)F,探究BP,DP,DF之間的數(shù)量關(guān)系,并證明.