抛物线C2:y^2=2px(p>0),
此抛物线焦点坐标F2为:(p/2,0),
抛物线C1:y=ax^2+bx,
此抛物线焦点坐标F1为:[-b/2a,(4ac-b^2+1)/4a]
∵抛物线C1:y=ax^2+bx与抛物线C2:y^2=2px(p>0)关于直线x+y=1对称,
有,-b/2a=0,(4ac-b^2+1)/4a=-(p/2),
b=0,1/4a=-p/2,
a=-1/p,
F1F2的中点坐标为:
而,F1(0,1/4a),a=-1/p,即F1为(0,-P/4).
F2(P/2,0),
X=(0+p/2)/2=p/4,y=(-p/4+0)/2=-p/8.
点X,Y在直线X+Y=1上,有
p/4-p/8=1,p=8.
a=-1/8.
即有:a=-1/8,b=0,p=8.
2).C1的焦点为F1(0,-2),抛物线C2的焦点为F2(4,0).
F1F2=√[(0-4)^2+(-2-0)^2]=2√5.
则,抛物线C1的焦点与抛物线C2的焦点之间的距离为:2√5.