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: 16

Answer

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.
1513549021

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.
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.