We give conceptual proofs of certain basic properties of the arrangement of shifted root hyperplanes associated to a root system R0 and a W0 = W (R0)-invariant real valued parameter function on R0. The method is based on the role of this shifted root hyperplane arrangement for the harmonic analysis of affine Hecke algebras. In addition this yields a conceptual proof of the description of the central support of the Plancherel measure of an affine Hecke algebra given by the author earlier.