已知雙曲線E:
=1(a>0,b>0)的離心率為2,左、右焦點(diǎn)分別為F
1(-c,0),F(xiàn)
2(c,0),點(diǎn)A(x
1,y
1)為雙曲線E右支上異于其頂點(diǎn)的動(dòng)點(diǎn),過(guò)點(diǎn)A作圓C:x
2+y
2=a
2的一條切線AM,切點(diǎn)為M,且|AM|
2+3=
x
-a
2.
(1)求雙曲線E的標(biāo)準(zhǔn)方程;
(2)設(shè)直線AF
1與雙曲線左支交于點(diǎn)B,雙曲線的右頂點(diǎn)為D(a,0),直線AD,BD分別與圓C相交,交點(diǎn)分別為異于點(diǎn)D的點(diǎn)P,Q.判斷弦PQ是否過(guò)定點(diǎn),如果過(guò)定點(diǎn),說(shuō)明理由.