Question

determine the equation of the circle graphed below.
answer attempt 1 out of 2
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Explanation:

Step1: Find the center of the circle

The center of the circle \((h,k)\) is \((1,-4)\) (by observing the graph, the point at the middle of the circle).

Step2: Find the radius of the circle

The radius \(r\) is \(3\) (distance from center \((1,-4)\) to a point on the circle, e.g., \((1,-1)\) or \((4,-4)\)).

Step3: Use the standard form of the circle equation

The standard form of a circle equation is \((x - h)^2+(y - k)^2=r^2\). Substitute \(h = 1\), \(k=-4\), and \(r = 3\) into the formula: \((x - 1)^2+(y+4)^2=9\)

Answer:

\((x - 1)^2+(y + 4)^2=9\)