Question

write the equation of the circle

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: Determine the center and radius from the graph

From the graph, the center of the circle is \((1,5)\) and the radius \(r = 2\) (since the distance from the center to a point on the circle is \(2\) units).

Step3: Substitute \(h = 1\), \(k = 5\), and \(r^2=4\) into the standard form

Substituting into \((x - h)^2+(y - k)^2=r^2\), we get \((x - 1)^2+(y - 5)^2=4\).

Answer:

\((x - 1)^2+(y - 5)^2=4\) (the blue - colored option)