Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 9 - Section 9.4 - Rotation of Axes - Exercise Set - Page 1011: 47

Answer

See graph and explanations.
1586022368

Work Step by Step

Step 1. Rewrite the equation as $6y^2+(4x)y+(3x^2-7)$ and let $a=6, b=4x, c=3x^2-7$ Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get $y=\frac{-4x\pm\sqrt {(4x)^2-4(6)(3x^2-7)}}{12}=\frac{-2x\pm\sqrt {42-14x^2}}{6}$ Step 3. We can graph the equations $y_1=\frac{-2x+\sqrt {42-14x^2}}{6}$ and $y_2=\frac{-2x-\sqrt {42-14x^2}}{6}$ as shown in the figure.
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