Question

determine the equation of the circle graphed below.
answer

Explanation:

Step1: Find the center of the circle

From the graph, the center of the circle \((h,k)\) is \((-4,-4)\).

Step2: Find the radius of the circle

By counting the units from the center to a point on the circle, the radius \(r = 2\).

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 \(h=-4\), \(k = -4\), and \(r = 2\) into the equation:

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Answer:

\((x + 4)^2+(y + 4)^2=4\)