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Questions: Algebra BusinessCalculus
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Find the center and radius of the circle \(\displaystyle \left(x - 3\right)^{2} + \left(y - 9\right)^{2}=121\).
Using the equation of a circle \(\displaystyle (x-h)^2+(y-k)^2=r^2\) to identify \(\displaystyle h,k,\) and \(\displaystyle r\) gives: \(\displaystyle h=3\), \(\displaystyle k=9\), and \(\displaystyle r=11\). The center is at \(\displaystyle (3,9)\) and the radius is \(\displaystyle r = 11\).
\begin{question}Find the center and radius of the circle $\left(x - 3\right)^{2} + \left(y - 9\right)^{2}=121$.
\soln{9cm}{Using the equation of a circle $(x-h)^2+(y-k)^2=r^2$ to identify $h,k,$ and $r$ gives: $h=3$, $k=9$, and $r=11$. The center is at $(3,9)$ and the radius is $r = 11$. }
\end{question}
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\begin{document}\begin{question}(10pts) The question goes here!
\soln{9cm}{The solution goes here.}
\end{question}\end{document}<p> <p>Find the center and radius of the circle <img class="equation_image" title=" \displaystyle \left(x - 3\right)^{2} + \left(y - 9\right)^{2}=121 " src="/equation_images/%20%5Cdisplaystyle%20%5Cleft%28x%20-%203%5Cright%29%5E%7B2%7D%20%2B%20%5Cleft%28y%20-%209%5Cright%29%5E%7B2%7D%3D121%20" alt="LaTeX: \displaystyle \left(x - 3\right)^{2} + \left(y - 9\right)^{2}=121 " data-equation-content=" \displaystyle \left(x - 3\right)^{2} + \left(y - 9\right)^{2}=121 " /> .</p> </p><p> <p>Using the equation of a circle <img class="equation_image" title=" \displaystyle (x-h)^2+(y-k)^2=r^2 " src="/equation_images/%20%5Cdisplaystyle%20%28x-h%29%5E2%2B%28y-k%29%5E2%3Dr%5E2%20" alt="LaTeX: \displaystyle (x-h)^2+(y-k)^2=r^2 " data-equation-content=" \displaystyle (x-h)^2+(y-k)^2=r^2 " /> to identify <img class="equation_image" title=" \displaystyle h,k, " src="/equation_images/%20%5Cdisplaystyle%20h%2Ck%2C%20" alt="LaTeX: \displaystyle h,k, " data-equation-content=" \displaystyle h,k, " /> and <img class="equation_image" title=" \displaystyle r " src="/equation_images/%20%5Cdisplaystyle%20r%20" alt="LaTeX: \displaystyle r " data-equation-content=" \displaystyle r " /> gives: <img class="equation_image" title=" \displaystyle h=3 " src="/equation_images/%20%5Cdisplaystyle%20h%3D3%20" alt="LaTeX: \displaystyle h=3 " data-equation-content=" \displaystyle h=3 " /> , <img class="equation_image" title=" \displaystyle k=9 " src="/equation_images/%20%5Cdisplaystyle%20k%3D9%20" alt="LaTeX: \displaystyle k=9 " data-equation-content=" \displaystyle k=9 " /> , and <img class="equation_image" title=" \displaystyle r=11 " src="/equation_images/%20%5Cdisplaystyle%20r%3D11%20" alt="LaTeX: \displaystyle r=11 " data-equation-content=" \displaystyle r=11 " /> . The center is at <img class="equation_image" title=" \displaystyle (3,9) " src="/equation_images/%20%5Cdisplaystyle%20%283%2C9%29%20" alt="LaTeX: \displaystyle (3,9) " data-equation-content=" \displaystyle (3,9) " /> and the radius is <img class="equation_image" title=" \displaystyle r = 11 " src="/equation_images/%20%5Cdisplaystyle%20r%20%3D%2011%20" alt="LaTeX: \displaystyle r = 11 " data-equation-content=" \displaystyle r = 11 " /> . </p> </p>