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: 9

Answer

$(h,k)=(\frac{1}{4},-\frac{1}{4})$ and $r= (\frac{\sqrt {10}}{4})$

Work Step by Step

An equation of the circle with center $(h,k)$ and radius $r$ is given as: $(x-h)^{2}+(y-k)^{2}=r^{2}$ ...(1) Given: $2x^{2}+2 y^{2}-x +y= 0$ The above equation can be written in the standard equation of the circle as follows: $(x-\frac{1}{4})^{2}+ (y-(-\frac{1}{4}))^{2} =(\frac{\sqrt {10}}{4})^{2}$ Compare it with equation (1), we have Hence, center,$(h,k)=(\frac{1}{4},-\frac{1}{4})$ and $r= (\frac{\sqrt {10}}{4})$
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