The Parabola as a Locus

Loading the math board and drawing, please wait…

2013-11-05 09:51

This example demonstrates the definition of a parabola as the locus of points equidistant from a focus and a directrix. It involves core concepts like parabola, focus, directrix, and distance. Constructed using commands such as Line, Point, OrthogonalLine, LineBisector, Intersect, LocusEquation, and Segment in GeoGebra. Suitable for high school coordinate geometry teaching and learning the properties of parabolas.

GeoGebra Commands & Parameters

Line(A, B) → directrix
Point(directrix) → P
OrthogonalLine(P, directrix) → p
LineBisector(Focus, P) → b
Intersect(p, b) → Q
LocusEquation(Q, P) → c
Segment(Focus, Q) → a_1
Segment(Q, P) → a_2

AI Drawing Prompt Reference

Draw a line as the directrix, take a point on the line, and draw the perpendicular line from the point to the directrix. Then, find the intersection of the perpendicular line with the line from the focus to the directrix, and draw the line from the focus to this intersection point. Finally, draw the locus of the intersection point as it moves, which forms a parabola. Show the focus, directrix, perpendicular line, intersection point, parabola, and the line from the focus to the intersection point.

The prompt above was compiled from the original drawing commands and is for reference only.