Question

determine the equation of the circle graphed below.

Explanation:

Step1: Identify the center of the circle

From the graph, the center of the circle is at the point \((h, k) = (4, -7)\) (by looking at the coordinates on the grid where the center lies).

Step2: Determine the radius of the circle

By counting the grid units from the center to the edge of the circle, we can see that the radius \(r = 2\) (since the distance from the center to the top, bottom, left, or right of the circle is 2 units).

Step3: Use the standard equation of a circle

The standard form of the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\). Substituting \(h = 4\), \(k = -7\), and \(r = 2\) into the equation, we get:

$$ (x - 4)^2 + (y - (-7))^2 = 2^2 $$

Simplifying the equation:

$$ (x - 4)^2 + (y + 7)^2 = 4 $$

Answer:

\((x - 4)^2 + (y + 7)^2 = 4\)