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.

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)