## Write-Up #6:

## Problems

### Different Methods of Constructing Parabolas

There are several methods of constructing parabolas. It can
be done by tracing a point which creates a parabola. A picture
of this construction looks like below.

Here, point C is always equidistant from the points D and F.
So, as Point F moves along the line the position of C changes
to remain equidistant. That change in postition has been traced
to create the parabola. Click **here**
to open a GSP sketch with an animation to create the above parabola.

A second method to create a parabola is to trace the lines
tangent to the parabola. This will create an envelope in the shape
of a parabola. A picture of this construction is below.

Here, the tangent line j has been traced in order to enclose
the parabola. Click **here**
to open a GSP sketch that will animate the construction.

A third option to create a parabola is to create the locus.
This can be done easily in GSP. Click **here**
to open a GSP file of this construction or a picture of the end
result is below.

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