## 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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