Let a ≥ b > 0 and set k = 2√ab/a − b. Show that the trochoid x = at − b sin t, y = a − b cos t, 0 ≤ t ≤ T has length 2(a − b)G(T/2, k), with G(θ, k) as in Exercise 30.

Data From Exercise 30

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Let a b and set k= Use a parametric representation to show that the ellipse ()+(² = 1 has length L = 4aG(, k), where C G(0,k) = is the elliptic integral of the second kind. b² √1 - k² sin² t dt