On Enlarging the Focal Point of a Parabola

  • On Enlarging the Focal Point of a Parabola

    Thomas Dence
    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.