The equation of a circle in a coordinate plane can be expressed in the standard form:
\[ (x - h)^2 + (y - k)^2 = r^2 \]
where \((h, k)\) is the center of the circle and \(r\) is the radius.
Given the center of the circle at \((5, 7)\) and a radius of \(3\):
- \(h = 5\)
- \(k = 7\)
- \(r = 3\)
Now, substituting these values into the equation:
\[ (x - 5)^2 + (y - 7)^2 = 3^2 \]
Calculating \(r^2\):
\[ 3^2 = 9 \]
Thus, the equation of the circle is:
\[ (x - 5)^2 + (y - 7)^2 = 9 \]
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