Question

question
determine the equation of the circle graphed below.
(graph of a circle on a coordinate plane with x-axis from -10 to 10 and y-axis from -10 to 10)

Explanation:

Step1: Find the center of the circle

From the graph, the center of the circle \((h,k)=(4,6)\)

Step2: Find the radius of the circle

Count the distance from the center to a point on the circle. The radius \(r = 4\)

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 \(h = 4\), \(k = 6\) and \(r = 4\) into the equation:

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Answer:

\((x - 4)^2+(y - 6)^2=16\)