In the example below, we can see parabolas that are made with criteria that they must always pass through a given point [math]\left(10,7\right)[/math] and should have a directrix represented by the line [math]\text{y=-9}[/math]. Notice that the path taken by the foci of these possible parabolas is a circle. This is to satisfy the definition of the parabola where each point in a parabola must maintain equal distance to the focus and to the directrix. Since this situation presents a fixed directrix, the focus must adjust to maintain the properties of a parabola. This is done by adjusting the focus to vertex directrix distance [math]a[/math] which can be controlled with the slider below.[br][br]Notice that the value of [math]a[/math] is bound with the condition [math]0<16\le16[/math] where when [math]a=0[/math], the parabolas degenerates into a line. When [math]a=16[/math], the parabolas merge into one. It has to be clear that this setup allows for infinite number of parabolas since [math]a[/math] is not limited to integers.