Quadratic Functions

So I was looking at different stuff about parabolas and discovered that reflections from a parabola all land in one spot. When light, or other rays all come in towards a parabola and hit off of the insides, they all reflect to one spot, called the focus. Here's what I mean:

As I continued researching the focus of a parabola, I learned that this is no coincidence. A parabola can be formed from a focus. You also need a directrix, a straight line. To form the parabola, you draw a whole bunch of points that are each equidistant from the directrix and the focus. Connecting these points will form a parabola.


However, all of the examples I found of this had the focus that wasn't on the directrix. So I thought about this and realized that a focus on a directrix would just be a point on a line. All of the points equidistant from the focus and directrix would just be on top of the focus. Does this mean that a point is actually a parabola?