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Parabola Right Side Construction

Parabola Right Side Construction
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2016-04-06 00:39
FunctionCoordinate GeometryOptimizationGeometric Construction
This example demonstrates the geometric construction and properties of the right side of a parabola. It involves core mathematical concepts like parabola definition, coordinate geometry, and geometric construction. GeoGebra commands and objects used include Segment, LineBisector, Point, Polygon, OrthogonalLine, Intersect, Locus, Line, Angle, Distance, etc. Suitable for high school mathematics teaching to understand parabola geometry and construction methods.

GeoGebra Commands & Parameters

  1. Segment(A, B) → a_2
  2. LineBisector(a_2) → n
  3. Point(n) → C
  4. Polygon(A, B, C) → poly1, c, a_1, b_1
  5. LineBisector(a_1) → d
  6. OrthogonalLine(C, n) → e
  7. Intersect(d, e) → P
  8. Locus(P, C) → f
  9. Intersect(n, a_2) → M
  10. Intersect(d, a_1) → E
  11. Segment(B, P) → f_1
  12. Segment(C, P) → g
  13. OrthogonalLine(E, a_2) → a
  14. Line(A, B) → b_2
  15. Intersect(a, b_2) → F
  16. Angle(B, M, C) → α
  17. Point(d) → G
  18. Angle(C, E, G) → β
  19. Point(f) → H
  20. Line(B, n) → b
  21. Parabola(B, n) → k
  22. Intersect(k, b, 2) → I
  23. Intersect(k, b, 1) → J
  24. Segment(I, J) → j
  25. Distance(A, B) → distanceAB
  26. Point(b) → D
  27. Distance(B, J) → distanceBJ

AI Drawing Prompt Reference

Draw a line segment and its perpendicular bisector. Mark a point on the bisector, then connect the segment's endpoints to this point to form a triangle. Find the intersection of the bisector with one side of the triangle, then draw a perpendicular line from this point to the other side, meeting it at another point. With one endpoint as the focus and the bisector as the directrix, sketch the right side of a parabola. Connect the focus to the intersection point and draw two lines from a point on the segment to this intersection. From one side of the triangle, draw a perpendicular line intersecting the segment, then another perpendicular line intersecting the other side. Draw two parallel lines from the segment, intersecting the parabola at two points, and connect these points. Label the segment length and draw lines from a point on the segment to the parabola's intersection point.
The prompt above was compiled from the original drawing commands and is for reference only.