# Geometric Locus

1. Sep 15, 2014

### 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.

2. Sep 17, 2014

### 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.