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: 7

Answer

a) Check graph. As t increases, y increases. As t increases, x initially increases and then decreases again back to its original position. b) $y=\sqrt(-x+1)-2$ or $x=-(y+2)^{2}+1$
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Work Step by Step

a) $x=1-t^{2}$, $y=t-2$, $-2 \leq t \leq 4$ When, t=-2 x=-3 y=-4 t=-1 x=0 y=-3 t=0 x=1 y=-2 t=1 x=0 y=-1 t=2 x=-3 y=0 t=3 x=-8 y=1 t=4 x=-15 y=1 b) $x=1-t^{2}$ $\sqrt (-x+1)=t$ $y=t-2$ $y=\sqrt(-x+1)-2$ or $x=-(y+2)^{2}+1$ From part A, we can infer that $-4 \leq y \leq0$
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