 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2013/paper-2/15/b/solution

The hyperbolic functions identity eliminates

t

\frac{x ^{2}}{a ^{2}} - \frac{y ^{2}}{b ^{2}} = 1, x \geq a .

The restriction is essential:

cosh t \geq 1

, so the parametrization traces only the right branch of the full hyperbola. Conversely, every point on that right branch is reached by taking

t = arsinh (y / b)

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