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: 34


$$x= -3+3t, \quad y= 4t.$$

Work Step by Step

First, we find the slope $m=\frac{4-0}{ 0+3}=\frac{4}{3}$. Now, we have $m=\frac{s}{r}=\frac{4}{3}$ so take $r=3$ and $s=4$. Then, the parametric equations are $$x=a+rt=-3+3t, \quad y= b+st= 4t.$$ That is, $$c(t)=(x(t),y(t))=(-3+3t,4t).$$
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