Question

determine the equation of the circle graphed below.

Explanation:

Step1: Find the center of the circle

From the graph, the center of the circle \((h,k)=(7, - 2)\)

Step2: Find the radius of the circle

Count the distance from the center to a point on the circle. The radius \(r = 2\)

Step3: Use the standard form of the circle equation

The standard form of a circle equation is \((x - h)^{2}+(y - k)^{2}=r^{2}\)
Substitute \(h = 7\), \(k=-2\) and \(r = 2\) into the equation:
\((x - 7)^{2}+(y+2)^{2}=4\)

Answer:

\((x - 7)^{2}+(y + 2)^{2}=4\)