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: 34

Answer

See image: .

Work Step by Step

Divide the equation with 2304 $ \displaystyle \frac{x^{2}}{36}-\frac{y^{2}}{64}=1,\ \quad$ We recognize the standard equation of a hyperbola. The foci are on the x-axis: $\quad \displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\quad a=6, \ b=8$ Center-to-focus distance: $\quad c=\sqrt{a^{2}+b^{2}}=\sqrt{36+64}=10$ Foci: $\quad (\pm c, 0)=\quad (\pm 10, 0)$ Vertices: $\quad (\pm a, 0)=\quad (\pm 6, 0)$ Asymptotes: $\quad y=\displaystyle \pm\frac{b}{a}x=\pm\frac{8}{6}x$ $y=\displaystyle \pm\frac{4}{3}x$
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