如图,在平面直角坐标系中,将一块腰长为 的等腰直角三角板 ABC 放在第二象限,且斜靠在两坐标轴上,直角顶点 C 的坐标为( ,0),点 B 在抛物线 上. (1)点 A 的坐标为 ,点 B 的坐标为 ; (2)抛物线的解析式为 ; (3)设(2)中抛物线的顶点为 D ,求△ DBC 的面积; (4)在抛物线上是否还存在点P(点B除外),使ΔACP仍然是以AC为直角边的等腰直角三角形?若存在,请直接写出所有点P的坐标;若不存在,请说明理由。
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