Distance to Focus
Parabola Passing Through a Given Point with a Given Directrix
In the example below, we can see parabolas that are made with criteria that they must always pass through a given point and should have a directrix represented by the line . 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 which can be controlled with the slider below.
Notice that the value of is bound with the condition where when , the parabolas degenerates into a line. When , the parabolas merge into one. It has to be clear that this setup allows for infinite number of parabolas since is not limited to integers.