X is the same as y.

Draw and describe the locus that is equidistant from end points (4,6) and (6,4). Write an equation for that locus.

ANSWER:

(x-2).(x-2) + (y-3).(y-3) = (x-4).(x-4)+(y-5).(y-5)

=>x.x + 4 - 4x + y.y + 9-6y = x.x + 16 - 8x + y.y + 25 - 10y

=>4 - 4x + 9 - 6y = 16 - 8x + 25 - 10y

=>13 - 4x - 6y = 41 - 8x - 10y

=>8x - 4x + 10y - 6y = 41

=>4x + 4y = 28

=> x + y = 7

(x-2).(x-2) + (y-3).(y-3) = (x-4).(x-4)+(y-5).(y-5)

=>x.x + 4 - 4x + y.y + 9-6y = x.x + 16 - 8x + y.y + 25 - 10y

=>4 - 4x + 9 - 6y = 16 - 8x + 25 - 10y

=>13 - 4x - 6y = 41 - 8x - 10y

=>8x - 4x + 10y - 6y = 41

=>4x + 4y = 28

=> x + y = 7