Question

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

Explanation:

Step1: Identify the center of the circle

Looking at the graph, the center of the circle is at \((h, k) = (-3, 0)\) (by observing the coordinates on the grid).

Step2: Determine the radius of the circle

The radius \(r\) can be found by counting the number of units from the center to the edge of the circle. From the center \((-3, 0)\) to the rightmost point or leftmost point, we can see the radius is \(3\) units (since the distance from \(x = -3\) to \(x = 0\) is \(3\), for example).

Step3: Use the standard equation of a circle

The standard equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\). Substituting \(h = -3\), \(k = 0\), and \(r = 3\) into the equation:

$$ (x - (-3))^2 + (y - 0)^2 = 3^2 $$

Simplifying this, we get:

$$ (x + 3)^2 + y^2 = 9 $$

Answer:

\((x + 3)^2 + y^2 = 9\)