What-If-Not Conic Constructions GGG 2017

Steve Phelps

This is a collection of investigations that explore small changes to the traditional conic constructions for the GeoGebra Global Gathering 2017


  • 1. What-If-Not Conic Constructions #1
  • 2. The Art of Problem Posing
  • 3. What-If-Not Conic Constructions #2
  • 4. What-If-Not Conic Constructions #3
  • 5. What-If-Not Conic Constructions #4
  • 6. What-If-Not Conic Construction #5
  • 7. What-If-Not Side-By-Side Construction
  • 8. What-If-Not Conic Constructions #6
  • 9. Conic Constructions Using Other Directrix

1.

What-If-Not Conic Constructions #1

The Parabola Construction
We begin with the construction of a parabola. Play through the construction. Drag the points so you understand how the parts of the construction behave.[br][br]A parabola is the locus of all points equidistant from a point and a line. We can also discuss [b]eccentricity[/b] which is the ratio of the these two distances [code][/code][code]Distance[F,P]:Distance[P,D].[br][/code].
There are four construction characteristics that might be interesting to investigate. [br][list][br][*]What happens if the perpendicular bisector is perpendicular, but is not a bisector?[br][/*][*]What happens if the perpendicular bisector is a bisector, but is not perpendicular?[/*][*]What happens if the perpendicular to the directrix constructed at D is not perpendicular?[br][/*][*]What happens if the directrix is not a line?[/*][/list]
– Steve Phelps

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