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Second-Order Implicit Function Locus

Second-Order Implicit Function Locus
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2019-02-20 12:00
FunctionCoordinate GeometryLocus
This example demonstrates the locus of a second-order implicit function. Key mathematical concepts include second-order functions, locus, center, and focus. Using GeoGebra commands such as FirstAxisLength, SecondAxisLength, Focus, and Center, the locus of the second-order implicit function is constructed. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. FirstAxisLength(conic) → AxisLength_1
  2. SecondAxisLength(conic) → AxisLength_2
  3. Focus(conic) → Focus_2, Focus_1
  4. Center(conic) → Center
  5. Asymptote(conic) → Asymptote_1, Asymptote_2
  6. Axes(conic) → Axis_1, Axis_2
  7. Determinant(Q) → DetQ
  8. Determinant(Φ) → DetΦ
  9. If(Determinant[Q] > 0 ∧ Determinant[Φ] ≠ 0, Text["ELLIPSE"]) → text3
  10. If(Determinant[Q] ≟ 0 ∧ Determinant[Φ] ≠ 0, Text["PARABOLA"]) → text4
  11. If(Determinant[Φ] ≟ 0, If[Determinant[Q] < 0, Text["INTERSECTING LINES"]]) → text6
  12. If(Determinant[Φ] ≠ 0, If[Determinant[Q] < 0, Text["HYPERBOLA"]]) → text1
  13. Vertex(conic) → Vertex_1, Vertex_2, Vertex_3, Vertex_4
  14. If(Determinant[Q] ≟ 0 ∧ Determinant[Φ] ≟ 0, Text["PARALLEL LINES"]) → text7
  15. Intersect(conic, Line[(0, 0), (-5, 0)]) → Root_1, Root_2
  16. Intersect(conic, Line[(0, 0), (0, 5)]) → Yintercept_1, Yintercept_2