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 636: 30


- the vertices are $(\pm 4,0)$ and $(0, \pm 2)$ - the foci are $(0, \pm \sqrt{12})$ - the center is $(0,0)$

Work Step by Step

The equation $4x^2+ y^2=16$ can be written in the form $$ \left(\frac{x}{2}\right)^{2}+\left(\frac{y}{4}\right)^{2}=1 $$ which is an ellipse with $a=2, b=4$ so $b\gt a$ and hence $ c=\sqrt{b^2-a^2}=\sqrt{16-4}=\sqrt{12}$. So, we have: the vertices are $(0,\pm 4)$ and $(\pm 2,0)$ the foci are $(0, \pm \sqrt{12})$ the center is $(0,0)$
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