Geometric recipes for constructing Bézier conics of given centre or focus

Concentric and confocal conics relate by linear and perspective maps, respectively. Using this property, we carry over the well-known quadratic Bézier construction of a circular arc to arbitrary conic segments of given centre C or focus F. First, choose arbitrarily the Bézier endpoints and assign them unitary weights. Second, pick the inner Bézier point on a certain line passing through C or F. The distance from C or F to this inner point determines the inner weight.