Question

write the equation of this circle in standard form.

Explanation:

Step1: Recall the standard form of a circle's 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: Identify the center of the circle

From the graph, the center of the circle is at \((6, 0)\) (since the green dot is at \(x = 6\), \(y = 0\)).

Step3: Determine the radius of the circle

Looking at the graph, the distance from the center \((6, 0)\) to the edge of the circle (e.g., to \(x = 9\) or \(x = 3\)) is \(3\) units (since \(9 - 6 = 3\) and \(6 - 3 = 3\)). So the radius \(r = 3\).

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

Substitute \(h = 6\), \(k = 0\), and \(r = 3\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - 6)^2 + (y - 0)^2 = 3^2\), which simplifies to \((x - 6)^2 + y^2 = 9\).

Answer:

\((x - 6)^2 + y^2 = 9\)