Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 44


For the right branch ($x>0$): $c(t)=(a \cosh t,b \sinh t)$. For the left branch ($x<0$): $c(t)=(-a \cosh t,b \sinh t)$.

Work Step by Step

From hyperbolic identity we have $\cosh^2 t-\sinh^2 t=1$. Thus, we may parametrize the hyperbola $(x/a)^2-(y/b)^2=1$ using $x=a \cosh t$ and $y=b \sinh t$, for $a$ and $b$ positive. Since $\cosh t$ is always positive, but $\sinh t$ is positive for $t>0$ and negative for $t<0$; for the right branch ($x>0$), the parametrization is $c(t)=(a \cosh t,b \sinh t)$ for $-\infty
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.