question_answer

Let ABC be a variable triangle such that A is (1,2), B and C lie on the line \[y=x+\lambda \] (where \[\lambda \] is a variable). The locus of the orthocentre of triangle ABC is a straight line whose y-intercept is equal to

A)  2                                

B)  3

C)  4                                

D)  5

Correct Answer: B

Solution :

            Clearly \[{{m}_{MA}}\,\times {{m}_{BC}}=-1\] \[\Rightarrow \,\,\frac{k-2}{h-1}\,\times 1=-1\] \[\Rightarrow \,k-2=1-h\] \[\therefore \] Locus of \[H(h,k)\] is \[x+y=3\]