The sum of the distance of the point P from the point (4,0) and the distance of P from the origin is 8 units .Show that the locus of P is the ellipse $\displaystyle \frac{(x-2)^2}{16}+\frac{y^2}{12}=1$

I started with :

Let P(x,y)

$\displaystyle \sqrt{(x-4)^2+(y^2)}+\sqrt{x^2+y^2}=8$

Then i am not sure what to do from here . .