ABC is a variable triangle such that A is (1,2), and B and C lie on the line y=x+λ (λ is a variable). Then the locus  of the orthocenter of △ABC is

Equation of line perpendicular to x-y+λ=0 and passing through (1,2) is x+y=3As the altitude from A is fixed and the orthocenter lies on the altitude, x + y = 3 is the required locus.