We begin with the construction of a parabola. Play through the construction. Drag the points so you understand how the parts of the construction behave.
A parabola is the locus of all points equidistant from a point and a line. We can also discuss eccentricity which is the ratio of the these two distances Distance[F,P]:Distance[P,D].
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There are four construction characteristics that might be interesting to investigate.

What happens if the perpendicular bisector is perpendicular, but is not a bisector?

What happens if the perpendicular bisector is a bisector, but is not perpendicular?

What happens if the perpendicular to the directrix constructed at D is not perpendicular?