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: 36


The parametric equation after the translation is $c(t)=(7+5\cos t,4+12\sin t)$

Work Step by Step

The ellipse of Exercise 28 is parametrized by $c(t)=(5\cos t,12\sin t)$ for $-\pi \leq t\leq \pi$. The center is at the origin. To translate the center of $c(t)$ at $(0,0)$ to $(7,4)$, we replace $c(t)=(5\cos t,12\sin t)$ by $c(t)=(7+5\cos t,4+12\sin t)$ for $-\pi \leq t\leq \pi$.
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