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 - Review Exercises - Page 699: 20

Answer

ellipse

Work Step by Step

The general equation of a conic in the form of $Ax^2+Bxy+Cy^2+Dx+Ey+F=0$ if $B=0$ (i) defines a parabola if $AC=0$ (ii) defines an ellipse if $AC\gt0$ and $A\ne C$ (iii) defines an a circle if $AC\gt0$ and $A=C$ (iv) defines a hyperbola if $AC\lt0$ Here $A=1,C=2$, hence $AC=2\gt0$ and $1\ne2$, thus it is an ellipse.
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