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: 49


See graph and explanations.

Work Step by Step

Step 1. Rewrite the equation as $16y^2+(24x-130)y+(9x^2+90x)$ and let $a=16, b=24x-130, c=9x^2+90x$ Step 2. Use the quadratic formula $y=\frac{-b\pm\sqrt {b^2-4ac}}{2a}$ to get $y=\frac{-24x+130\pm\sqrt {(24x-130)^2-4(16)(9x^2+90x)}}{32}=\frac{-12x+65\pm\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$ Step 3. We can graph the equations $y_1=\frac{-12x+65+\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$ and $y_2=\frac{-12x+65-\sqrt {(12x-65)^2-16(9x^2+90x)}}{16}$ as shown in the figure.
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