On the tangential quadrilateral of the ellipse and hyperbole (Q2730589)

In this article the well-known necessary and sufficient condition \(a_1+a_3=a_2+a_4\) on the tangential convex quadrilateral of the circle is generalized to ellipse and hyperbole. Namely, if \(d_j, j=\overline{1,4}\) denotes the distance between the centre of the considered conic section and the side \(a_j, j=\overline{1,4}\) of the convex tangential quadrilateral, then it is NEWLINE\[NEWLINE d_1a_1+d_3a_3=d_2a_2+d_4a_4.NEWLINE\]NEWLINE This generalized condition is just necessary (only in the circle case it becomes sufficient as well).