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Parabola Inversion

Parabola Inversion
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2015-06-16 03:05
FunctionCoordinate GeometryGeometric Construction
This example demonstrates the inversion transformation of a parabola and its resulting geometric changes. Key math concepts include inversion transformation, parabolic geometric properties, and analytical geometry. Construction highlights involve using GeoGebra commands such as Intersect, Point, Circle, and Mirror to build necessary geometric objects like b, a, A, B, c, d, d', C, C'. Suitable for high school and above students to explore the application of inversion in analytical geometry.

GeoGebra Commands & Parameters

  1. Intersect(xAxis, yAxis) → A
  2. Point(yAxis) → B
  3. Circle(A, B) → c
  4. Mirror(d, c) → d'
  5. Point(d) → C
  6. Mirror(C, c) → C'

AI Drawing Prompt Reference

Draw a parabola and its inversion transformation. Start by plotting the intersection of the coordinate axes, then draw a circle centered at this point with radius equal to the distance to another point on the axis. Reflect the circle across a line passing through the center and the other point. Find the intersection of the line and the reflected circle, then reflect this point across the original circle. Connect these points to form the transformed shape, highlighting the geometric changes due to inversion.
The prompt above was compiled from the original drawing commands and is for reference only.