已知點(diǎn)A(-1,0),B(1,0),動(dòng)點(diǎn)P(x,y)滿足:PA與PB的斜率之積為3.設(shè)動(dòng)點(diǎn)P的軌跡為曲線E.
(1)求曲線E的方程;
(2)記點(diǎn)F(-2,0),曲線E上的任意一點(diǎn)C(x
1,y
1)滿足:x
1<-1,x
1≠-2且y
1>0,設(shè)∠CFB=α,∠CBF=β.
①求證:tanα=tan2β;
②設(shè)過(guò)點(diǎn)C的直線
x=-y+b與軌跡E相交于另一點(diǎn)D(x
2,y
2)(x
2<-1,y
2<0),若∠FCB與∠FDB互補(bǔ),求實(shí)數(shù)b的值.