Conic Directrix and Focus Demonstrator
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This example dynamically demonstrates the relationship between the focus and directrix of conic sections (ellipse, hyperbola) using a slider. It involves core mathematical concepts like the definition of conic sections, eccentricity, directrix, and focus. Construction highlights include using GeoGebra commands If, Directrix, Eccentricity, Text with objects such as a, d, ecc, b, conic, d1, d2, i, h, ecc2, g, f, text1. Suitable for high school coordinate geometry teaching or self-learning to understand the generation principles of conic sections.
GeoGebra Commands & Parameters
If(ecc < 1, sqrt(1 - ecc^(2)), sqrt(ecc^(1))) → bIf(ecc < 1, x^(2) / a^(2) + y^(2) / b^(2) = 1, x^(2) / a^(2) - y^(2) / b^(2) = 1) → conicDirectrix(conic) → i, hEccentricity(conic) → ecc2If(a ≟ b, y = (-x)) → gIf(a ≟ b, y = x) → fText(("eccentricity = " * ecc2)) → text1