Precalculus (10th Edition)

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

Chapter 10 - Analytic Geometry - 10.5 Rotation of Axes; General Form of a Conic - 10.5 Assess Your Understanding - Page 679: 51



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 $A=3,B=-2,C=1$, hence $B^2-4AC=(-2)^2-4(3)(1)=4-12=-8\lt0$ and $3\ne1, thus it is an ellipse.
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