A
parabola is the locus of all points equidistant from a
given point, the *focus*, and a line, the **
***directrix*.
The
September 2011 issue of The College Mathematics Journal
(published by MAA) contains an article by Dan Joseph,
Gregory Hartman and Caleb Gibson titled Generalized
Parabolas (available online if a member/subscriber or
through jstor:
http://www.jstor.org/pss/10.4169/college.math.j.42.4.275
if you have access to jstor). In their article they investigate what happens if you
change the directrix in the definition above to a
general curve, for example, a parabola (see example 3
below). The authors took an analytical approach, using
Mathematica to find the equation of each generalized
parabola.
I
recognized GeoGebra could be used for a purely
geometrical investigation. Examples 3 through 11 below
reproduce examples from the paper sited above.
The
routine that produced the examples below is available
for use
here.
Example 1 gives some
instructions on using the generalized parabolas GeoGebra
manupulative. |