Question

If two points (2, 3) and ( - 6, - 5) are equidistant from the point ( x , y ) , show that x + y + 3 = 0 .

Answer 1

√{(x-2)² + (y-3)²} = √{(x+6)² + (y+5)²}
x² + 4 - 4x + y² + 9 - 6y = x² + 36 + 12x + y² + 25 + 10y
16x + 16y + 48 = 0
x + y + 3 = 0         prove