Hyperbola Equation Parameters and Translation Demo
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This example demonstrates how the hyperbola defined by -((x-l)/a)^2 + ((y-m)/b)^2 = 1 changes shape and position as its parameters vary. It covers hyperbola equations, center translation, semi-axis lengths, and coordinate geometry graphing. The construction uses objects a, b, l, m to control horizontal and vertical scaling and the center coordinates, while h_1 and h render the hyperbola curve, making it easy to observe the effects on opening, vertices, and asymptotic behavior. It is suitable for high-school analytic geometry, conic sections, and GeoGebra graphing exploration.
GeoGebra Commands & Parameters
Numeric a(0.8)Numeric b(0.9)Numeric l(0.0)Numeric m(2.6)((x - l) / a)^(2) - ((y - m) / b)^(2) = 1-((x - l) / a)^(2) + ((y - m) / b)^(2) = 1
AI Drawing Prompt Reference
Draw a hyperbola with sliders to control horizontal and vertical scaling parameters, and the center coordinates, showing how the hyperbola's shape and position change with varying parameters, and observe the dynamic effects on the vertices and asymptotes.
The prompt above was compiled from the original drawing commands and is for reference only.