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 \((h, k) = (3, 0)\) (by looking at the coordinates on the grid).

Step3: Determine the radius of the circle

The radius \(r\) is the distance from the center to the edge of the circle. From the graph, the radius is \(1\) unit (since the circle spans from \(x = 2\) to \(x = 4\) or \(y = -1\) to \(y = 1\), so the radius is \(1\)).

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

Substitute \(h = 3\), \(k = 0\), and \(r = 1\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - 3)^2 + (y - 0)^2 = 1^2\), which simplifies to \((x - 3)^2 + y^2 = 1\).

Answer:

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