Playing with the parabola in the Poincaré disk

What exists below is an interactive construction of a parabola in the Poincaré disk. The focus is the point F and the directrix is the line through points A and B. You can move the directrix by moving the points A and B and you can move the focus. As you move the focus and directrix, you will see the parabola change (though it may take a few seconds). To be clear, the parabola is pink.