Question

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the equation of a circle is $(x - 10)^2+(y - 8)^2 = 256$
what is the center of the circle?
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Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle and \(r\) is the radius.

Step2: Identify \(h\) and \(k\)

Given the equation \((x - 10)^2+(y - 8)^2=256\), by comparing with \((x - h)^2+(y - k)^2=r^2\), we can see that \(h = 10\) and \(k = 8\).

Answer:

\((10,8)\)