Sentence:  More generally, the locus of points z such that \left\vert x - z \right\vert = \alpha\left\vert y - z \right\vert is a <WSD>circle of Apollonius</WSD> which has x and y as inverse points and which cuts each circle through x and y orthogonally....They show loci analogous to <WSD>circles of Apollonius</WSD> and the locus of points equidistant from two given points when the norm is an \mathcal{l}_p-norm. 
Meaning of the word marked with <WSD> tags:  (geometry) The figure (a generalised circle) definable as the locus of points "P" such that, for given points "A", "B" and "C", <small>\frac{|AP|}{|BP|} = \frac{|AC|}{|BC|}</small>.