Question

question determine the equation of the circle graphed below.

Explanation:

Step1: Recall the circle equation formula

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: Identify the center coordinates

From the graph, the center of the circle is at \((h, k)=(-2, 1)\) (by observing the grid and the position of the circle's center).

Step3: Determine the radius

The radius is the distance from the center to any point on the circle. By counting the grid units, the radius \(r = 3\) (since the distance from the center \((-2, 1)\) to a point on the circle, like \((1, 1)\) or \((-2, 4)\), is 3 units).

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

Substitute \(h=-2\), \(k = 1\), and \(r = 3\) into \((x - h)^2 + (y - k)^2 = r^2\):

$$ (x - (-2))^2 + (y - 1)^2 = 3^2 $$

Simplify the left - hand side and the right - hand side:

$$ (x + 2)^2 + (y - 1)^2 = 9 $$

Answer:

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