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 the equation of a circle is \((x - h)^2 + (y - k)^2 = r^2\), where \((h, k)\) is the center of the circle and \(r\) is the radius.

Step2: Determine the center of the circle

From the graph, the center of the circle is at the point \((8, -7)\). So, \(h = 8\) and \(k = -7\).

Step3: Determine the radius of the circle

Looking at the graph, the radius (the distance from the center to any point on the circle) is 1 unit (since the circle spans 1 unit in the x or y direction from the center). So, \(r = 1\).

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

Substitute \(h = 8\), \(k = -7\), and \(r = 1\) into \((x - h)^2 + (y - k)^2 = r^2\). We get \((x - 8)^2 + (y - (-7))^2 = 1^2\), which simplifies to \((x - 8)^2 + (y + 7)^2 = 1\).

Answer:

\((x - 8)^2 + (y + 7)^2 = 1\)