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The Inverse of a Parabola

The Inverse of a Parabola
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2015-04-26 10:25
FunctionCoordinate GeometryOptimization
This example demonstrates the inverse of a parabola and its geometric transformations. Key math concepts include inverse functions, geometric transformations, linear functions, and coordinate geometry. Construction involves GeoGebra commands like Line, Parabola, Circle, Point, Polygon, Mirror, and Locus. Suitable for high school students learning about inverse function properties and geometric meanings.

GeoGebra Commands & Parameters

  1. Line(A, B) → a
  2. Parabola(F, a) → c
  3. Circle(O_c, D) → d
  4. Point(c) → M
  5. Polygon(Corner[1], (x(Corner[1]) + (0.37 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.37 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → Left, b, e, f, g
  6. Mirror(M, d) → M'
  7. Locus(M', M) → loc1

AI Drawing Prompt Reference

Draw a parabola with a focus and a directrix line. Then construct a circle as the inversion circle. Pick a point on the parabola, reflect it about the circle to get its inverse point, and trace the locus of this inverse point as the original point moves along the parabola, producing a new curve. Also include a rectangular region on the left side as a visual reference. The final figure should show the parabola, the inversion circle, the moving point and its inverse, the traced locus, and the auxiliary rectangle, illustrating the geometric transformation of inversion.
The prompt above was compiled from the original drawing commands and is for reference only.