Question

determine the equation of the circle graphed below.

Explanation:

Step1: Recall the circle equation

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

Step2: Find the center \((h, k)\)

From the graph, the center of the circle is at \((-6, 6)\) (by identifying the coordinates of the center on the grid).

Step3: Determine the radius \(r\)

By counting the grid units from the center to the edge of the circle, the radius is \(2\) (since the distance from \(-6\) to \(-4\) (or \(-8\)) is \(2\), and similarly for the \(y\)-axis).

Step4: Substitute \(h\), \(k\), and \(r\) into the equation

Substitute \(h = -6\), \(k = 6\), and \(r = 2\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - (-6))^2 + (y - 6)^2 = 2^2\), which simplifies to \((x + 6)^2 + (y - 6)^2 = 4\).

Answer:

\((x + 6)^2 + (y - 6)^2 = 4\)