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Chord of a Parametric Parabola

Chord of a Parametric Parabola
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2016-10-24 11:47
FunctionCoordinate GeometryParametric Equation
This example demonstrates the chord of a parametric parabola. It involves the parametric equation of a parabola, midpoints, and chords. Using GeoGebra commands such as Point, OrthogonalLine, Parabola, Segment, and Midpoint, dynamic exploration of the properties of a parametric parabola can be achieved. Suitable for high school mathematics education, particularly for coordinate geometry and parametric equations.

GeoGebra Commands & Parameters

  1. Point(yAxis) → A
  2. OrthogonalLine(A, yAxis) → f
  3. Point(yAxis) → B
  4. Parabola(B, f) → c
  5. Point(c) → P
  6. Point(c) → Q
  7. Segment(P, Q) → g
  8. Midpoint(B, A) → C
  9. Segment(C, B) → a

AI Drawing Prompt Reference

Draw a parametric parabola and show a chord. First, plot the parabola. Then find two points on the parabola and connect them to form a chord. Next, find two points on the line containing the parabola, draw a line perpendicular to this line, and let it intersect the parabola at one point. Finally, connect the two points on the parabola and find the midpoint of the two known points, then connect the midpoint to one of the points.
The prompt above was compiled from the original drawing commands and is for reference only.