过定点A(-2,-4)作倾斜角为45°的直线l:x=y+2,①
与抛物线y^2=2px②交于B,C两点,
把①代入②,y^2-2py-4p=0,
设B(x1,y1),C(x2,y2),则
y1+y2=2p,y1y2=-4p,
AB ,BC,AC成等比数列,
(y2-y1)^2=(y1+4)(y2+4),
(y1+y2)^2=5y1y2+4(y1+y2)+16,
4p^2=-20p+8p+16,
p^2+3p-4=0,
p=1,或-4.
1.抛物线的方程为y^2=2x或y^2=-8x.
2.（i){x=y+2,
.{y^2=2x,
解得（x,y)=(3+√5,1+√5）或（3-√5,1-√5）,为B,C的坐标.
设D(2t^2,2t),由DB=BC得
[2t^2-(3+√5)]^2+[2t-(1+√5）]^2=40,
4t^4-4(3+√5）t^2+14+6√5+4t^2-4(1+√5）t+6+2√5=40,
4t^4-(8+4√5)t^2-(4+4√5)t+8√5-20=0,