直线y=2x与抛物线y^2=px+32(p>0)交于A,B两点,线段AB的垂直平分线过点Q(-5,5),求P值

y=2x,代入
4x^2-px-32=0
所以x1+x2=p/4
交点坐标(x1,y1),(x2,y2)
AB垂直平分线上的点到A和B距离相等
所以(-5-x1)^2+(5-y1)^2=(-5-x2)^2+(5-y2)^2
25+10x1+x1^2+25-10y1+y1^2=25+10x2+x2^2+25-10y2+y2^2
(x1^2-x2^2)+10(x1-x2)-10(y1-y2)+(y1^2-y2)^2=0
(x1+x2)(x1-x2)+10(x1-x2)-10(y1-y2)+(y1+y2)(y1-y2)=0
(x1+x2)(x1-x2)+10(x1-x2)-10(2x1-2x2)+(2x1+2x2)(2x1-2x2)=0
(x1+x2)(x1-x2)-2(x1-x2)=0
(x1-x12)(x1+x2-2)=0
若x1=x2,则y1=y2,是同一个点,不成立
所以x1+x2=2
p/4=2
p=8