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Locus Equation of the Cissoid Curve

Locus Equation of the Cissoid Curve
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2016-11-02 06:24
Coordinate GeometryParametric EquationGeometric ConstructionLocus
In collections Locus Line Equations demos
This example demonstrates the geometric construction and the resulting locus equation of a Cissoid curve. It focuses on the core mathematical concepts of coordinate geometry and the definition of loci. The construction is implemented using GeoGebra commands such as Point, Ray, and Intersect to establish the geometric constraints, and leverages the LocusEquation and Locus commands to derive and visualize the curve's path. This tool is ideal for high school students studying analytic geometry or undergraduate students exploring classical algebraic curves.

GeoGebra Commands & Parameters

  1. Point(a) → A
  2. Ray(O, A) → b
  3. Intersect(c, b, 2) → B
  4. Intersect(Circle[O, Distance[A, B]], b) → C,
  5. LocusEquation(C, A) → d
  6. Locus(C, A) → lieu1

AI Drawing Prompt Reference

Draw a ray starting from the origin and passing through a point. Find the intersection of this ray with a circle centered at the origin, whose radius is the distance between the first point and the intersection point. Then, determine the locus equation of the intersection point relative to the first point and plot this locus.
The prompt above was compiled from the original drawing commands and is for reference only.