Multivariable Calculus, 7th Edition

Published by Brooks Cole
ISBN 10: 0-53849-787-4
ISBN 13: 978-0-53849-787-9

Chapter 10 - Parametric Equations and Polar Coordinates - 10.1 Exercises - Page 665: 16


a) $\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$ $x \geq \sqrt 2$ $y \geq 0$ b) As t increases, x also increases, so the arrow should be pointing in the direction that x increases in.

Work Step by Step

a) Given: $x=\sqrt (t+1)$ Isolate t: $x^{2}=t+1$ $x^{2}-1=t$ Isolate t in the second equation: $y=\sqrt (t-1)$ $y^{2}=t-1$ $y^{2}+1=t$ Put the two equations together: $x^{2}-1=y^{2}+1$ $x^{2}-y^{2}=2$ $\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$ Domain: $x \geq \sqrt 2$ Range: $y \geq 0$ b) We know, $\frac{x^{2}}{2}-\frac{y^{2}}{2}=1$ $x \geq \sqrt 2$ $y \geq 0$ Now graph. It should be in the first quadrant. As t increases, so does x.
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