Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 10 - Analytic Geometry - Chapter Review - Chapter Test - Page 701: 9



Work Step by Step

The general equation of a conic in the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ (i) defines a parabola if $B^2-4AC=0$ (ii) defines an ellipse if $B^2-4AC\lt0$ and $A\ne C$ (iii) defines a circle if $B^2-4AC\lt0$ and $A= C$ (iv) defines a hyperbola if $B^2-4AC\gt0$ Here, we have $A=1,B=-6,C=9$ Hence, $B^2-4AC=(-6)^2-4(1)(9)=36-36=0$ Thus, it is a parabola.
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