Hello, xwrathbringerx!
Looks like you need a walkthrough . . . hints don't seem to work.
Show that the locus of a point, which moves so as always to be
three times further from one fixed point than from another fixed point, is a circle.
Since this claim is made for any two points,
. . place the points on the xaxis, symmetric to the origin. Code:
 P
 o (x,y)
 * *
*  *
*  *
  o     +     o  
(a,0)  (a,0)
A  B

Let be any point such that: .
Using the Distance Formula: .
Then: .
Square both sides: .
Expand: .
Simplify: .
Divide by 8: .
Complete the square: .
. . And we have: .
This is a circle with center and radius