MathPlotAI Logo MathPlotAI

Conic Eccentricity Slider

Conic Eccentricity Slider
Loading the math board and drawing, please wait…
2019-03-01 11:00
TrigonometryCoordinate GeometrySlider Animation
This example demonstrates the changes in eccentricity of conic sections. Key mathematical concepts include ellipses, hyperbolas, and the eccentricity of conic sections. Using GeoGebra commands such as If, Directrix, Cone, and Focus, the example dynamically shows how eccentricity affects the shape of the curves. Suitable for high school mathematics education and learning.

GeoGebra Commands & Parameters

  1. If(ecc1 ≥ 1, x^(2) / a^(2) - y^(2) / f^(2) = 1, x^(2) / a^(2) + y^(2) / b^(2) = 1) → conic
  2. Directrix(conic) → h, g
  3. If(f ≟ a, y = x) → i
  4. If(ecc1 ≟ 1, x = y^(2)) → para
  5. If(ecc1 ≟ 1, Directrix[para]) → paradirect
  6. If(ecc1 < 1.44 ∧ ecc1 > 1.38, y = (-x)) → j
  7. If(ecc1 < 1.44 ∧ ecc1 > 1.38, y = x) → k
  8. Cone((0, 0, 8), (0, 0, 0), 4) → e, e_2, e_3
  9. Cone((0, 0, -8), (0, 0, 0), 4) → l, l_2, l_3
  10. If(ecc1 ≟ 0, Plane[(0, 0, 6), (0, 1, 6), (1, 1, 6)], Plane[(2, 0, 6), x = (1 / ((2 * ecc1)) * z)]) → n
  11. Focus(conic) → F_1, F_2
  12. If(ecc1 ≟ 1, Focus[para]) → F