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 \((8, 0)\) (since it's on the x - axis at \(x = 8\) and \(y = 0\)).

Step3: Determine the radius of the circle

Looking at the graph, the circle extends from \(x = 7\) to \(x = 9\) (or we can count the grid units). The distance from the center \((8,0)\) to the edge is 1 unit, so the radius \(r = 1\).

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

Substitute \(h = 8\), \(k = 0\), and \(r = 1\) into \((x - h)^2+(y - k)^2=r^2\). We get \((x - 8)^2+(y - 0)^2 = 1^2\), which simplifies to \((x - 8)^2+y^2 = 1\).

Answer:

\((x - 8)^2 + y^2 = 1\)