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Locus of Midpoint of PB

Locus of Midpoint of PB
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2015-09-17 08:48
FunctionCoordinate GeometryGeometric ConstructionLocus
In collections Properties of the Parabola
This example demonstrates the locus of the midpoint of the line segment joining a point on the parabola to the y-intercept of the normal at that point. It involves core concepts like parabola, normal, midpoint, and locus. GeoGebra commands and objects used include Point, Tangent, Line, Intersect, and Midpoint. Suitable for high school and above students to explore analytical geometry and locus problems.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Tangent(P, c) → b,
  3. Line(P, F) → d
  4. Intersect(b, yAxis) → B
  5. Midpoint(P, B) → M

AI Drawing Prompt Reference

Draw a parabola and select a point P on it. Construct the tangent line b at P and the line d through P and the focus F of the parabola. Find the intersection B of b and the y-axis. Connect P and B to find the midpoint M. Observe the locus of M as P moves along the parabola.
The prompt above was compiled from the original drawing commands and is for reference only.