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Parabola with Center (h,k) and Focus at (k+p)

Parabola with Center (h,k) and Focus at (k+p)
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2017-04-13 03:32
FunctionCoordinate GeometryGeometric Construction
This example demonstrates a parabola with center (h,k) and focus at (k+p). Key mathematical concepts include the definition and properties of parabolas. Using GeoGebra commands, the focus, directrix, and vertex of the parabola can be constructed. Suitable for high school math education, this example helps students understand the geometric construction and properties of parabolas.

GeoGebra Commands & Parameters

  1. Numeric h(-0.05)
  2. Numeric k(-1.6)
  3. Numeric p(-2.05)
  4. (x - h)^(2) = ((4 * p) * (y - k))
  5. (h, k + p)
  6. y = k - p
  7. (h, k)

AI Drawing Prompt Reference

Draw a parabola with vertex at (h,k) and focus at (k+p), showing the focus, directrix, and vertex. Start by plotting the parabola defined by (x-h)^2=(4p)(y-k), then mark the focus and vertex, and finally draw the directrix y=k-p.
The prompt above was compiled from the original drawing commands and is for reference only.