Two vertices of a Triangle are (1,3) and (4,7). If its orthocentre lies on the line x+y=3, then the locus of third vertex is

Let A be (x,y) and orthocentre be α,3-α∵BO⊥BC⇒y−7x−4.α1−α=−1.........(1)∵AO⊥BC⇒y−3+αx−α×43=−1.........(2)Eliminating α from equation (1) and (2) we get option (3)