Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 11: Parametric Equations and Polar Coordinates - Section 11.6 - Conic Sections - Exercises 11.6 - Page 678: 12

Answer

Focus: $(-\displaystyle \frac{1}{2},0)\quad$ Directrix: $x=\displaystyle \frac{1}{2}$ .

Work Step by Step

$y^{2}=-4px \quad \Rightarrow \quad $the parabola opens left, $y^{2}=-2x$ $y^{2}=-2(\displaystyle \frac{4}{4})x$ $y^{2}=-4(\displaystyle \frac{1}{2})x \quad \Rightarrow \quad p=\frac{1}{2}$ Focus: $(-\displaystyle \frac{1}{2},0)\quad$ Directrix: $x=\displaystyle \frac{1}{2}$
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