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: 76


Equation of a circle with center $\left( -7,-4 \right)$ and radius $4$ is${{\left( x+7 \right)}^{2}}+{{\left( y+4 \right)}^{2}}=16$

Work Step by Step

Draw a circle with center $\left( -7,-4 \right)$ tangent to the y-axis. From the figure we see that the circle touches the y-axis at $\left( -7,0 \right)$. Since the radius is the distance between $\left( -7,0 \right)$ and $\left( -7,-4 \right)$. $\sqrt{{{\left( -7-\left( -7 \right) \right)}^{2}}+{{\left( -4-\left( 0 \right) \right)}^{2}}}$ $r=4$ Put the value of radius $4$ and center coordinate$ \left( -7,-4 \right)$ in the standard equation of the circle: $\begin{align} & {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \\ & {{\left( x-\left( -7 \right) \right)}^{2}}+{{\left( y-\left( -4 \right) \right)}^{2}}={{\left( 4 \right)}^{2}} \\ & {{\left( x+7 \right)}^{2}}+{{\left( y+4 \right)}^{2}}=16 \end{align}$ Thus, the equation of the circle with center $\left( -7,-4 \right)$ and radius $4$ is ${{\left( x+7 \right)}^{2}}+{{\left( y+4 \right)}^{2}}=16$.
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