Question

write an equation for the locus of ponits equipstant from lines y=6 and x=2

Answer 1

The distances from any point (x,y) to the lines y=6 and x=2 are |x-2| and |y-6|. If these two are equal, then |x-2|=|y-6|. Thus, \[y-6=\pm(x-2)\] then get two equations for y.

Answer 2

These equations are y=x+4 and y=-x+8..