Proving the Locus of Points Satisfying an Equation is a Circumference

[rulo1992]

The problem is: Let A, B and C be fixed points, and α,β,γ and κ are given constants, then the locus of a point P that satisfies the equation α(AP)²+β(BP)²+γ(CP)²=K, is a circunference. Prove it.

I need at least some hint to answer it, I tried using the distance between two points formula but I only get a mess of variables that show me nothing.

 

[haruspex]

I'm not familiar with the use of the word circumference to describe a locus. To me, it means the distance around a figure, not the shape of the figure. Please define how it is being used here.