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Tangent Line and Parabola Interaction Demo

Tangent Line and Parabola Interaction Demo
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2013-08-21 07:03
FunctionCoordinate GeometryDerivativeGeometric Construction
This example demonstrates the dynamic process of moving a tangent line on a parabola and finding its equation. It involves core mathematical concepts such as parabola, derivative, tangent line equation, and coordinate geometry. The construction uses GeoGebra commands like Intersect, Line, Point, Tangent, and OrthogonalLine. Suitable for high school students and above to learn the application of derivatives in geometry, and for calculus teaching demonstrations.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Line(B, A) → a
  3. Point(yAxis) → C
  4. Tangent(D, d) → b, c
  5. Intersect(d, b, 1) → E
  6. Intersect(d, c, 1) → F
  7. Point(xAxis) → G
  8. Point(xAxis) → H
  9. Line(G, H) → e
  10. OrthogonalLine(E, e) → f
  11. Intersect(a, f) → I
  12. Intersect(d, a, 2) → J
  13. Point(b) → K
  14. Line(E, K) → h

AI Drawing Prompt Reference

Draw a parabola with a dynamically movable tangent line showing its equation. First, identify the intersection points of the parabola with the coordinate axes and draw the parabola. Then, select a point on the y-axis and draw a horizontal line from it. Choose a point on the parabola, draw the tangent line at that point, and find the intersection of the tangent line with the horizontal line. Finally, draw a perpendicular line through the intersection point and display the equation of the tangent line and the coordinates of the intersection points.
The prompt above was compiled from the original drawing commands and is for reference only.