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Definition of Parabola by ged1182

Definition of Parabola by ged1182
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2019-05-09 20:13
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the definition of a parabola as the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). Key mathematical concepts include parabola, triangles, distance, orthogonal lines, intersections, and angles. It is constructed using GeoGebra commands and objects such as Line, Point, Parabola, Segment, Distance, OrthogonalLine, Intersect, Angle, and Circle. Suitable for high school coordinate geometry education or self-study to understand the geometric properties of parabolas.

GeoGebra Commands & Parameters

  1. Line(A, B) → directrix
  2. Point(yAxis) → Focus
  3. Parabola(Focus, directrix) → c
  4. Point(c) → P
  5. Segment(P, Focus) → f
  6. Distance(P, directrix) → distanceDdirectrix
  7. OrthogonalLine(P, directrix) → g
  8. Intersect(directrix, g) → E
  9. Segment(P, E) → h
  10. Angle((2.940557036199606, -2), (2.940557036199606, -2), (2.940557036199606, -2)) → α
  11. Angle(directrix, g) → γ
  12. Circle(P, Focus) → d

AI Drawing Prompt Reference

Draw a parabola defined by a focus and a directrix. First, draw a line as the directrix, then set a focus on the y-axis. Next, construct a parabola using the focus and directrix. Then, pick a point P on the parabola, draw a segment from P to the focus, and draw a perpendicular line from P to the directrix, finding the foot of the perpendicular E. Draw a segment from P to E, measure the distance from P to the directrix and the angle between the directrix and the perpendicular line. Finally, draw a circle with P as the center and the focus on the circumference.
The prompt above was compiled from the original drawing commands and is for reference only.