Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 12 - Parametric Equations, Polar Coordinates, and Conic Sections - 12.1 Parametric Equations - Exercises - Page 603: 30


$$x= 2+3t, \quad y= 5-t.$$

Work Step by Step

First, since the line is perpendicular to $y=3x$, then the slope is given by $-\frac{1}{3}$. Now, the slope $m=-\frac{1}{3}$; then, we have $s/r=-\frac{1}{3}$ so take $r=3$ and $s=-1$. Then, the parametric equations are $$x=a+rt=2+3t, \quad y= b+st=5-t.$$ That is, $$c(t)=(x(t),y(t))=(2+3t,5-t).$$
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