B,C都在抛物线y^2=4x上
可设B(x1,y1) C(x2,y2)
向量AB*向量AC=0
{x1-1,y1-2}*{x2-1,y2-2}=0
(y1^2/4-1)*(y2^2/4-1)+(y1-2)*(y2-2)=0
(y1-2)(y2-2)*[(y1+2)*(y2+2)/16+1]=0
y1≠2 y2≠2
则(y1+2)*(y2+2)/16+1=0
y1y2+2(y1+y2)=-20①
直线BC
y-y1=[(y1-y2)/(x1-x2)]*(x-x1)
y-y1=[(y1-y2)/(y1^2/4-y2^2/4)]*(x-x1)
y-y1=[4/(y1+y2)]*(x-x1)
y(y1+y2)=4(x-x1)+y1(y1+y2)
y(y1+y2)=4x-y1^2+y1^2+y1y2
y(y1+y2)=4x+y1y2
和①式对比知
过定点(5,-2)