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: 39


The conic section is an ellipse.

Work Step by Step

Comparing the given equation with the standard equation $$ a x^{2}+b x y+c y^{2}+d x+e y+f=0 $$ we get $a=4,b=5,c=7$. Now, we check the discriminant $$D=b^2-4ac=25-112=-87\lt 0$$ Since the discriminant is negative, the conic section is an ellipse.
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