General equation for taxicab conics and their classification (Q2764589)

In the real plane \(R^2\) endowed with the taxicab metric \(d_T\) point sets are investigated which fall under following type: \(\{X\in R^2\mid d_T(X,b_1)\circ d_T(X,b_2)= \text{const}\}\) where \((b_1,b_2)\) is a pair of points (foci) or a point-line pair or a pair of lines (directrices) and \(\circ\in\{+,-,:\}\). The authors restrict their discussion to the foci-sum, the foci-difference and the focus-directrix-ratio case. Most of the corresponding sets are composed either of line segments or of planar regions or of both. NEWLINENEWLINENEWLINEThe reviewer means that in taxicab geometry also the foci-ratio, the focus-directrix-sum, focus-directrix-difference, the directrices-sum and the directrices-difference case would deserve the same interest; the remaining directrices-ratio case yields a pair of lines.