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 855: 56


Center of circle is $\left( -3,2 \right)$ and radius is $r=\sqrt{28}$

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 ${{x}^{2}}+{{y}^{2}}+6x-4y=15$ (equation -2) Now add $4$ and $9$ on both the sides of (equation -2) to complete the square twice. $\begin{align} & {{x}^{2}}+{{y}^{2}}+6x-4y+9+4=15+9+4 \\ & \left( {{x}^{2}}+6x+9 \right)+\left( {{y}^{2}}-4y+4 \right)=28 \\ & {{\left( x+3 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{\left( \sqrt{28} \right)}^{2}} \end{align}$ Now compare the standard equation with the equation${{\left( x+3 \right)}^{2}}+{{\left( y-2 \right)}^{2}}={{\left( \sqrt{28} \right)}^{2}}$. Center coordinate of circle is $\left( h=-3,k=2 \right)$. And radius of circle is $r=\sqrt{28}$. To graph, we plot the points $\left( -3,7.292 \right)$, $\left( -3,-3.292 \right)$, $\left( -8.292,2 \right)$, and $\left( 2.292,3 \right)$ which are, respectively, $\sqrt{28}$ units above, below, left and right of $\left( -3,2 \right)$.
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