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Section 13.1: Vector Functions and Space Curves

Exercise 51

  1. Graph the curve with parametric equations \(x = \frac{27}{26}\sin 8t - \frac{8}{39}\sin 18t\) \(y = -\frac{27}{26}\cos 8t + \frac{8}{39}\cos 18t\) \(z = \frac{144}{65}\sin 5t\)
  2. Show that the curve lies on the hyperboloid of one sheet \(144x^2+144y^2-25z^2=100\).