Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 281: 91

Answer

The given statement is false. The correct statement is, “The graph of ${{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36$ is the equation of a circle with radius 6 centered at $\left( 3,-5 \right)$.”

Work Step by Step

The standard equation of a circle that has center $\left( h,k \right)$ and radius $r$ is ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$. Write the standard form of the equation as shown below: $\begin{align} & {{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36 \\ & {{\left( x-3 \right)}^{2}}+{{\left( y-\left( -5 \right) \right)}^{2}}={{6}^{2}} \end{align}$ Comparing to the standard equation, we get $\left( h,k \right)=\left( 3,-5 \right)$ and the radius is 6. Thus, the statement is false. The correct statement is, “The graph of ${{\left( x-3 \right)}^{2}}+{{\left( y+5 \right)}^{2}}=36$ is the equation of a circle with radius 6 centered at $\left( 3,-5 \right)$.”
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