There are many things you can create using any line in space and any point not on the line. One of which is a parabola! In fact, with every line and every point not on that line, there exists a unique parabola. The parabola is created by connecting the accumulation of the infinite number of points that lie exactly equidistant to the line (the shortest distance to this line) and the given point. Parabolas of varying narrownesses and widenesses have been created and analyzed as a result of this construction. It was fascinating to me to construct a parabola in this way in Geometer's Sketchpad alongside some of my classmates who are all studying how to best use technology in the classroom as future educators.
Once again, you will have to download Geometer's Sketchpad in order to view the attached exploration.
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