Central quadrics in Euclidean n-space - metric and focal properties

In this paper metric properties of central quadrics and cones in n -dimensional Euclidean space are discussed. Basic statements on the system of confocal regular quadrics are proved, and some interesting analogues of famous three-dimensional theorems are given for higher dimension, such as the Apollonian theorem on pedal curves. We also investigate systems of focal cones, and in particular we determine the common lines of focal cones in any dimension. As further applications of our approach and of our formulas we give a detailed description of the construction of Chasles on conjugate diameters, and the wire model of Staude is also given.