y=ax+13x^2-y^2=13x^2-(ax+1)^2=1(3-a^2)x^2-2ax-2=0xA+xB=2a/(3-a^2),(xA+xB)/2=a/(3-a^2)yA+yB=a(xA+xB)+2=6/(3-a^2),(yA+yB)/2=3/(3-a^2)AB两点关于直线y=3x对称,则[(xA+xB)/2,(yA+yB)/2]在直线y=3x上[(yA+yB)/2]/[(xA+xB)/2]=[6/(3-a^2)]/[2a/(3-a^2)]=3/a=3a=1,点[(xA+xB)/2,(yA+yB)/2]在直线y=3x上,但a=1时,AB不垂直y=3x,故不存在实数a,使得AB两点关于直线y=3x对称
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