The value of a for which the image of the point a,a−1 w.r.t. the line mirror 3x+y=6a is the point a2+1,a is

Image of point P in line AB is Q.Thus, L is the midpoint of AB.∴L≡a2+a+12,2a−12Since L lies on line AB.⇒ 3a2−7a+2=0∴  a=2,13Also, PQ⊥AB.⇒ −3×1a2−a+1=−1⇒ a2−a−2=0∴  a=2,−1