Plotting the Parabola in the Hyperbolic Upper Half-Plane

Here we have a graph of the parabola in the Hyperbolic Upper Half-Plane. We can manipulate the graph by moving the focus, F, and the directrix, line AB, to see in real time the resulting parabola. Points A, B, and F may be moved around in the space above the x-axis. We can also move point E to see how the parabola could be traced. The hyperbolic parabola is in pink.