Amaths - locus problem

Let P(x,y)

Then
PA=√[(x-2)^2+(y+1)^2]
PB=√[(x-2)^2+(y-1)^2]

|PA-PB| = 5
PA-PB=5 or -5

if PA-PB=5
√[(x-2)^2+(y+1)^2]=5+√[(x-2)^2+(y-1)^2]
(x-2)^2+(y+1)^2=25+10√[(x-2)^2+(y-1)^2]+(x-2)^2+(y-1)^2
4y=25+10√[(x-2)^2+(y-1)^2]
16y^2-200y+625=100x^2-400x+400+100y^2-200y+100
125=100x^2-400x+84y^2
100x^2+84y^2-400x-125=0

if PA-PB=-5
√[(x-2)^2+(y+1)^2]=-5+√[(x-2)^2+(y-1)^2]
(x-2)^2+(y+1)^2=25-10√[(x-2)^2+(y-1)^2]+(x-2)^2+(y-1)^2
4y=25-10√[(x-2)^2+(y-1)^2]
16y^2-200y+625=100x^2-400x+400+100y^2-200y+100
125=100x^2-400x+84y^2
100x^2+84y^2-400x-125=0

So we have the equation of the locus of P is

100x^2+84y^2-400x-125=0