Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 10 - Parametric Equations and Polar Coordinates - 10.5 Conic Sections - 10.5 Exercises - Page 720: 48


$\dfrac{5(y-4)^{2}}{16}-\dfrac{5(x-2)^{2}}{64}=1$; equation of a hyperbola.

Work Step by Step

From asymptotes we have $\frac{a}{b}=\frac{1}{2}$ or, $2a=b$ and $a^2+b^2=c^2$ or, $a^2+(2a)^2=4^2$ $a=\frac{4}{\sqrt 5}$ and $b=2a=2(\frac{4}{\sqrt 5})=\frac{8}{\sqrt 5}$ Hence, $\dfrac{5(y-4)^{2}}{16}-\dfrac{5(x-2)^{2}}{64}=1$; equation of a hyperbola.
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