equation of the locus of a point.

I need help because I got stuck on this problem :

Find the equation of the locus of a point P = (x,y) that moves in accordance with each of the following conditions, and sketch the graphs:

a. The sum of the squares of the distances from P to the points (a,0) and (-a,0) is 4b^2, where b >= a/sqrt of 2 > 0

b. the distance of P from the point (8,0) is twice its distance from the point (0,4).

what ive done so far :

I think B is a line between the points (0,4) and (8,0) with a slope of 2/1. 2/1 is the negative reciprical of the line that goes threw (0,4) and (8,0)

So y=2X+B is the line I get for P according to the second guideline (b.).

Y and x of the point P must both work out to this formula so I should be able to substitute y for 2x+B in the equation I get from Part a of this problem. :

(x-a)^2+y^2+(x+a)^2+y^2=4B^2 =

(x-a)^2+(2x+B)^2+(x+a)^2+(2x+B)^2=4b^2 =

10x^2+2a^2+8xb-2b^2 = 0

Now I have the equation of some point I guess. But I dont know how to solve it from here. All I can think to do is simplify it all by dividing by 2. but then I get stuck. Someone please help.