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: 50


See graph and explanations.

Work Step by Step

Step 1. Rewrite the equation as $4y^2+(4x)y+(x^2+10\sqrt 5x-9)$ and let $a=4, b=4x, c=x^2+10\sqrt 5x-9$ Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get $y=\frac{-4x\pm\sqrt {(4x)^2-4(4)(x^2+10\sqrt 5x-9)}}{8}=\frac{-x\pm\sqrt {9-10\sqrt 5x}}{2}$ Step 3. We can graph the equations $y_1=\frac{-x+\sqrt {9-10\sqrt 5x}}{2}$ and $y_2=\frac{-x-\sqrt {9-10\sqrt 5x}}{2}$ as shown in the figure.
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