Abstract
Given points p and q in the plane, we are interested in separating them by two curves C_1 and C_2 such that every point of C_1 has equal distance to p and to C_2, and every point of C_2 has equal distance to C_1 and to q. We show by elementary geometric means that such C_1 and C_2 exist and are unique.
Moreover, for p=(0,1) and q=(0,-1), C_1 is the graph of a function f, C_2 is the graph of -f, and $f$ is convex and analytic. We provide an algorithm that, given x, in polynomial time approximates f(x) with a given precision.