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On Enlarging the Focal Point of a Parabola

Thomas Dence 

May 2005, Volume 98, Issue 9, Page 594

Abstract:
The geometry and algebra behind what happens when the definition of a parabola is changed by altering the size of the focal point. Different types of problems may open a wealth of related explorations including describing the locus of points equidistant from a line or describing the locus of points whose distances from two given circles sum to a constant. Students have the opportunity to be creative with their investigations and perhaps discover some interesting mathematical relationships.

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Grades 9-12
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