Hyperbola Standard Function Demo
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This example demonstrates the standard function graph of a hyperbola and its parameter variations. Core math concepts include hyperbola definition, standard equation, and the influence of parameters a and b on the graph shape. GeoGebra commands/objects used: objects c(constant), a(real axis semi-length), f(focus), b(虚轴半长), d(vertex distance), ϕ(angle parameter). Suitable for high school analytic geometry teaching and function graph research.
GeoGebra Commands & Parameters
Numeric c(1.2)Numeric a(0.94)f: abs(sqrt((x + c)^(2) + y^(2)) - sqrt((x - c)^(2) + y^(2))) = (2 * a)sqrt(c^(2) - a^(2))Numeric d(1.98)x^(2) / a^(2) - y^(2) / d^(2) = 1
AI Drawing Prompt Reference
Draw a standard hyperbola graph. The hyperbola is centered at the origin, with foci on the x-axis. Parameters a and b determine the shape. Vertices are on the x-axis, and asymptotes are straight lines. Ensure the graph is clear and labeled with key points like foci and vertices.
The prompt above was compiled from the original drawing commands and is for reference only.