Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 9 - Analytic Geometry - Section 9.5 Rotation of Axes; General Form of a Conic - 9.5 Assess Your Understanding - Page 698: 14



Work Step by Step

If $B=0$ and $A $ and $C$ are not both zero, then the general equation of a conic has the form of $Ax^2+Cy^2+Dx+Ey+F=0(1)$ (a) When $AC=0$, then a conic defines a parabola. (b) When $AC \gt 0$, then a conic defines an ellipse and $A\ne C$ (c) When $AC \gt 0$, then a conic defines a Circle and $A=C$ (d) When $AC \lt 0$, then a conic defines a hyperbola. We have: $A=2,C=1$. Plug these values in Equation (1) to obtain: $AC=(2)(1)=2 \gt 0$,and $6 \ne 3$, so the conic represents an Ellipse.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.