1. ## ellipse

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 $\frac{(x-2)^2}{16}+\frac{y^2}{12}=1$

I started with :

Let P(x,y)

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

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

2. You have it. Isolate one radical then square both sides. Then do it again. It's tedious, but it works.

You DO need to worry about Doamin issues while doing this sort of thing, but the whole design of this problem is nicely positive, so it should be fine.