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

From the graph, the center of the circle is at \((-3, 0)\) (since it's on the x - axis, \(y = 0\), and the x - coordinate is - 3).

Step3: Find the radius

The radius is the distance from the center to the top (or bottom) of the circle. The center is at \(y = 0\), and the top of the circle is at \(y = 3\) (or we can count the grid units). So the radius \(r=3\).

Step4: Substitute into the equation

Substitute \(h=-3\), \(k = 0\), and \(r = 3\) into the standard form: \((x-(-3))^2+(y - 0)^2=3^2\), which simplifies to \((x + 3)^2+y^2 = 9\).

Answer:

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