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 - Chapter Review Exercises - Page 638: 12


$$ y=\pm \sqrt{1+x^2}.$$

Work Step by Step

We have $x=\tan t$, $y=\sec t$. Use the trig identity: $$1+\tan^2 t=\sec^2t$$ Combine with $x$ and $y$: $$y^2=1+x^2.$$ Solve for $y$: $$ y=\pm \sqrt{1+x^2}.$$
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