A parabola is the set of points equidistant from a line, called the directrix, and a fixed point, called the focus. Assume the focus is not on the line. Construct a parabola given a fixed point for the focus and a line (segment) for the directrix.
á Use an Action Button to generate the parabola from an animation and trace of a constructed point.
á Repeat 9a with a trace of the tangent line at the constructed point.
á Use the locus command to generate the parabola from a constructed point or the tangent line at that point.
LetŐs construct a line segment, called the directrix, a point not on the line, called the Focus, and a point N on the directrix:
Next, construct a segment from our focus to point N on the directrix.
Now, letŐs construct a perpendicular bisector from the directrix to the focus and take the midpoint of the newly constructed line. Then construct a perpendicular line through that point and the newly constructed line, giving you the perpendicular bisector.
Next, construct a perpendicular line through point N on the directrix and label the intersection of the perpendicular line through point N and the perpendicular bisector, C.
Finally, moving the point N along the directrix causes the point C to move along the perpendicular bisector and perpendicular line creating a Parabola shown below: