Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 13 - Conic Sections - 13.1 Conic Sections: Parabolas and Circles - 13.1 Exercise Set - Page 854: 53

Answer

Center of circle is $\left( 5,0 \right)$ and radius is $r=\frac{1}{2}$.

Work Step by Step

Standard equation of the circle is: ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ (equation - 1) And equation of circle is ${{\left( x-5 \right)}^{2}}+{{y}^{2}}=\frac{1}{4}$ (equation - 2) Now compare both the equations. $\begin{align} & {{\left( x-5 \right)}^{2}}+{{y}^{2}}=\frac{1}{4} \\ & {{\left( x-\left( 5 \right) \right)}^{2}}+{{\left( y-\left( 0 \right) \right)}^{2}}={{\left( \frac{1}{2} \right)}^{2}} \\ \end{align}$ Center coordinate of circle is $\left( h=5,k=0 \right)$. And radius of the circle is $r=\frac{1}{2}$. To graph, we plot the points $\left( 5,0.7071 \right)$, $\left( 5,-0.7073 \right)$, $\left( 4.293,0 \right)$, and $\left( 5.707,0 \right)$ which are, respectively, $\frac{1}{2}$ units above, below, left and right of $\left( 5,0 \right)$.
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