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 - 12.5 Conic Sections - Exercises - Page 635: 5


The vertices are $(3\pm7,-1)$. The foci are $(3\pm \sqrt{65},-1)$.

Work Step by Step

The equation $$ \left(\frac{x-3}{7}\right)^{2}-\left(\frac{y+1}{4}\right)^{2}=1 $$ is hyperbola with center $(3,-1)$. We have $a=7$, $b=4$, $c=\sqrt{a^2+b^2}=\sqrt{65}$ and hence: When the center is at the origin, the foci are $(\pm \sqrt{65},0)$ and the vertices are $(\pm 7,0).$ Then the translation by $(3,-1)$ gives The new vertices are $(3\pm7,-1)$. The new foci are $(3\pm \sqrt{65},-1)$.
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