We have two perpendicular lines - like the axes of an ellipse - and a tangent $(t)$ with its point of tangency $(T)$. Construct the endpoints of the ellipse's axes $(A, B, C, D)$! How many solutions are there?
Let the tangent touch one of the axes at $P$; draw a circle over the diameter $\overline{O P}$ and project $T$ perpendicularly onto this circle in the direction of $|O P|$. $\overline{O T_{1}}$ is the radius of the affine circle from which we obtain $\overline{A B}$ and $\overline{C D}$ as shown in the figure. There is one solution.

Sándor Gyula (Kölcsey Ferencg. VIII. o. Budapest)