Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - Review - True-False Quiz: 7

Answer

False

Work Step by Step

The first pair of equations only gives the right half of the parabola , that is, $y=x^{2}$. whereas the second pair of equations traces outs the whole parabola. For example: First case: when $x=t^{2}, y=t^{4}$ Then $(x,y)=(1,1)$ at $t=1$ and $(x,y)=(1,1)$ at $t=-1$ Second case: when $x=t^{3}, y=t^{6}$ Then $(x,y)=(1,1)$ at $t=1$ and $(x,y)=(-1,1)$ at $t=-1$ Thus, the second pair of equations traces outs the whole parabola , that is, $y=x^{2}$. Hence, the given statement is false.
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