(Solution) - The ends of an elastic string with a knot at -(2025 Original AI-Free Solution)

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Academic Level: Undergrad. (yrs 3-4)

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The ends of an elastic string with a knot at K(x, y) are attached to a fixed point A(a, b) and a point P on the rim of a wheel of radius r centered at (0,0), As the wheel turns. K traces a curve C. Find the equation for C. Assume that the string stays taut and stretches uniformly (i.e., a = |KP| / |AP| is constant).