Assignment
6
Investigation
9
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.
Answer:
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:
9a)
9b)
9c)
