`A B C` is a variable triangle such that `A` is (1, 2), and `Ba n dC` on the line `y=x+lambda(lambda` is a variable). Then the locus of the orthocentre of `"triangle"A B C` is `x+y=0` (b) `x-y=0` `x^2+y^2=4` (d) `x+y=3`

Options

A. x+y=0
B. x-y=0
C. `x^(2) + y^(2)=4`
D. x+y=3

Answer

D

Explanation

As the altitude from A is fixed and the orthocenter lies on the altitude, x+y=3 is the required locus.