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: 32


$$x= \frac{1}{3}+t, \quad y= \frac{1}{6}-t.$$

Work Step by Step

First, we find the slope $m=\frac{\frac{10}{6}-\frac{1}{6}}{-\frac{7}{6}-\frac{2}{6}}=\frac{9}{-9}=-1$. Now, we have $m=\frac{s}{r}=-1$ so take $r=1$ and $s=-1$. Then, the parametric equations are $$x=a+rt=\frac{1}{3}+t, \quad y= b+st=\frac{1}{6}-t.$$ That is, $$c(t)=(x(t),y(t))=(\frac{1}{3}+t,\frac{1}{6}-t).$$
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