The question is what is the equation that includes the points T so that the distance from T to O = (4,0,1) is twice the distance from T to C = (1, -2, 4)?

I set the equation up like this $\displaystyle sqrt((x-4)^2 + (y-0)^2 + (z-4)^2) = 2sqrt((x-1)^2 + (y+2)^2 + (z-4)^2)$

I get it down to this:

$\displaystyle x^2 + (y + 16/6)^2 + (z - 5)^2 = -137/9$

The problem is the equation doesn't work because the second side is negative