A parabola is the set of points equidistant from a line, called the directrix, and a fixed point, called the focus.
Assuming that the focus is a point not on the line. A construction of a parabola can be made using the focus and and the directrix.
Here is a construction of a parabola given these points on GSP.
The result of this construction and animating a point of the directrix, a parabola can be formed using the trace feature.
Here is the construction of the parabola and the trace of the tangent line of the parabola as the point at the directrix varies. GSP.
