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: 1

Answer

$(2,6), (0,2), (0,0), (2,0),$ and $(6,2)$ are consecutive points on the curve. The arrow points from $(2,6)$ to $(6,2)$.
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Work Step by Step

Since $-2 \leq t \leq 2,$ plot the points where $t=-2,$ $t=-1,$ $t=0,$ $t=1,$ and $t=2$. You can find the $x$ and $y$ coordinates of each point by plugging the value of $t$ into the given formulas for $x$ and $y$. For instance, when $t=-2,$ $$x = (-2)^2 + (-2) = 2$$$$y = (-2)^2 - (-2) = 6$$ Therefore, $t=-2$ corresponds to the point $(2,6)$. The same calculation gives: $(0,2)$ for $t=-1$ $(0,0)$ for $t=0$ $(2,0)$ for $t=1$ $(6,2)$ for $t=2$ Plot these five points and connect them with a curve (in order of increasing $t$), as shown. As $t$ increases from $-2$ to $2$, the curve is traced from $(2,6)$ to $(6,2)$, so an arrow should be drawn on the curve in that direction, as shown.
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