Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

Find the equation of the locus of a point P(x,y) such that PV = PW, where V = (1,1) and W = (3,5)

Answer Details

The locus of a point P(x,y) such that PV = PW where V = (1,1) and W = (3,5). This means that the point P moves so that its distance from V and W are equidistance.
PV = PW
$\sqrt{(x-1{)}^2+(y-1{)}^2}=\sqrt{(x-3{)}^2+(y-5{)}^2}$.
Squaring both sides of the equation,
(x-1)2 + (y-1)2 = (x-3)2 + (y-5)2.
x2-2x+1+y2-2y+1 = x2-6x+9+y2-10y+25
Collecting like terms and solving, x + 2y = 8.