Question

write the standard form of the equation of the circle with the graph shown to the right.
what is the standard form of the equation of the circle to the right?
(simplify your answer.)

Explanation:

Step1: Identify circle center

From the graph, the center \((h,k)\) is \((5, -6)\).

Step2: Determine radius length

Count grid units: radius \(r = 2\).

Step3: Use circle standard formula

Standard form: \((x-h)^2 + (y-k)^2 = r^2\). Substitute \(h=5\), \(k=-6\), \(r=2\):
\((x-5)^2 + (y-(-6))^2 = 2^2\)

Step4: Simplify the equation

Simplify signs and \(r^2\):
\((x-5)^2 + (y+6)^2 = 4\)

Answer:

\((x-5)^2 + (y+6)^2 = 4\)