Question: A particle moves along a path modeled by where b is a positive constant. (a) Show that the path of the particle is a hyperbola.

A particle moves along a path modeled by

r(t) = cosh(bt)i + sinh(bt)j

where b is a positive constant.

(a) Show that the path of the particle is a hyperbola.

(b) Show that a(t) = b² r(t).

r(t) = cosh(bt)i + sinh(bt)j

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