problem with polynomials and spheres

[markcholden]

Hi all,

I've got this problem:

Consider the points P such that the distance from P to A(-1,5,3) is twice the distance from P to B(6,2,-2). Show that the set of all such points is a sphere, and find its center and radius.

I think the setup should be this:

sqrt[(x+1)^2 + (y-5)^2 + (z-3)^2] = 2*sqrt[(x-6)^2 + (y-2)^2 + (z+2)^2]

But when I try to work it out, I just end up with a mess and no equation for a sphere. Any help appreciated.

(Note: This is a problem from my calculus class, but since there's really no calculus involved, I posted it here. Sorry if that was a mistake.)

 

[tkhunny]

Have you considered working with this:

(x+1)^2 + (y-5)^2 + (z-3)^2 = 4*[(x-6)^2 + (y-2)^2 + (z+2)^2]