Find an equation in x and y in general form?

Question

Find an equation in x and y in general form such that the distance between (x,y) and (3,1) is twice the distance between (x,y) and (-2,0)

Answer 1

the distance between (x,y) and (3,1) =

sqrt[(x-3)^2+(y-1)^2]

the distance between (x,y) and (-2,0) =

sqrt[(x+2)^2+y^2]

sqrt[(x-3)^2+(y-1)^2] = 2 sqrt[(x+2)^2+y^2]

square both sides

(x-3)^2+(y-1)^2 = 4 (x+2)^2+y^2

x^2-6x+9 + y^2-2x+1 = 4[ x^2+4x+4 +y^2]

x^2-6x+9+y^2-2y+1-4x^2-16x-16-4y^2=0

-3x^2-3y^2-22x-2y-6=0

This is the general form

You can also write this as

3x^2+3y^2+22x+2y+6=0