Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Appendix C - Graphs of Second-Degree Equations - C Exercises: 26

Answer

Ellipse

Work Step by Step

Given: $16x^{2}+9y^{2}-36y=108$ By completing the square, we get $16x^{2}+9(y^{2}-4y+4)=108+9(4)$ $16x^{2}+9(y-2)^{2}=144$ Divide by $144$. $\frac{x^{2}}{9}+\frac{(y-2)^{2}}{16}=1$ which is the standard form of the equation of a Ellipse. $\frac{(x-h)^{2}}{b^{2}}+\frac{(y-k)^{2}}{a^{2}}=1$ Here, $(h,k)=(0,2)$
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