Rolling Parabola Trajectory
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This example demonstrates the locus of a parabola's focus, involving arc lengths, parabolic properties, and hyperbolic functions. Using the CurveCartesian command in GeoGebra, the trajectory can be dynamically observed. Suitable for high school mathematics, particularly in coordinate geometry and calculus courses.
GeoGebra Commands & Parameters
CurveCartesian((a / sqrt(1 + t^(2)) * ((2 * u) + (t * u^(2)) - t + (sqrt(1 + t^(2)) * asinh(t)))), (a * (u - t)^(2) / sqrt(1 + t^(2))), u, -10, 10) → b
AI Drawing Prompt Reference
Draw the trajectory of a parabola's focus defined by parameters u and t. The x-coordinate is a/t * ((2*u) + (t*u^2) - t + (sqrt(1 + t^2) * asinh(t))), and the y-coordinate is a * (u - t)^2 / sqrt(1 + t^2), with u ranging from -10 to 10.
The prompt above was compiled from the original drawing commands and is for reference only.