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: 37


${{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18$

Work Step by Step

Standard equation of the circle is: ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ Where, the center coordinates are $\left( h,k \right)$ and $\left( x,y \right)$ is any point on the circumference and $r$ is the radius of the circle. $\begin{align} & {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \\ & {{\left( x-\left( -4 \right) \right)}^{2}}+{{\left( y-\left( 3 \right) \right)}^{2}}={{\left( 3\sqrt{2} \right)}^{2}} \\ & {{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=9\cdot 2 \\ & {{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18 \end{align}$ The equation of the circle with center $\left( -4,3 \right)$ and radius $3\sqrt{2}$ is ${{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18$.
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