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Hyperbola as a Vector Sum of Two Lines

Hyperbola as a Vector Sum of Two Lines
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2015-07-22 00:26
VectorFunctionCoordinate Geometry
This example demonstrates how a hyperbola can be formed as the vector sum of two lines, inspired by Scratchard graphs in chemistry. Key mathematical concepts include vectors and coordinate geometry. It utilizes commands such as Line, Point, Ray, Intersect, Sequence, Conic, and Focus. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Line(C, D) → b
  3. Point(a) → E
  4. Ray((0, 0), E) → c
  5. Intersect(b, c) → F
  6. Sequence(Intersect[x = i, a], i, 0, 4) → list1
  7. Sequence(Intersect[Line[(0, 0), Element[list1, i]], b], i, 1, 5) → list2
  8. Conic(Element[list3, 1], Element[list3, 2], Element[list3, 3], Element[list3, 4], Element[list3, 5]) → d
  9. Focus(d) → H, I
  10. Intersect(a, b) → J
  11. Line(I, H) → e
  12. Intersect(d, e, 2) → K
  13. Intersect(d, e, 1) → L