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Locus of Tangent Midpoint of an Ellipse

Locus of Tangent Midpoint of an Ellipse
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2017-11-27 21:48
Coordinate GeometryLocus
This example demonstrates the locus of the midpoint of a tangent to an ellipse. Key mathematical concepts include ellipse, symmetry, right triangles, and straight lines. Using GeoGebra commands such as Point, Tangent, Line, Intersect, and Midpoint, the construction of the locus of the tangent midpoint is illustrated. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. Point(c) → P
  2. Tangent(P, c) → f,
  3. Point(yAxis) → B_1
  4. Point(yAxis) → C
  5. Line(B_1, C) → g
  6. Point(xAxis) → D
  7. Point(xAxis) → E
  8. Line(D, E) → h
  9. Intersect(f, g) → B
  10. Intersect(h, xAxis) → G
  11. Intersect(f, h) → A
  12. Midpoint(B, A) → M

AI Drawing Prompt Reference

Draw an ellipse and select a point P on it. Construct the tangent line f at point P. Choose two points B₁ and C on the y-axis and draw line g through them. Choose two points D and E on the x-axis and draw line h through them. Find the intersection B of line f and g, the intersection G of line h and the x-axis, and the intersection A of line f and h. Find the midpoint M of segment BA. Observe the locus of point M.
The prompt above was compiled from the original drawing commands and is for reference only.