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: 16



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: $A=4,C=-3$ Plug these values in Equation (1) to obtain: $AC=(4)(-3)=-12 \lt 0$, so the conic represents a hyperbola.
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