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: 41


The conic section is a hyperbola.

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 $a=2,b=-8,c=3$. Now, we check the discriminant $$D=b^2-4ac=64-24=40\gt 0$$ Thus, the conic section is a hyperbola.
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