Question

write the equation of the circle graphed below.
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Explanation:

Step1: Find the center of the circle

The center of the circle (purple dot) has coordinates \((h,k)=(-2,-2)\)

Step2: Find the radius of the circle

The radius \(r\) is the distance from the center \((-2,-2)\) to the point on the circle (blue dot) \((-1,-2)\). Using the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), we have \(r=\sqrt{(-1-(-2))^2+(-2 - (-2))^2}=\sqrt{(1)^2+(0)^2}=1\)

Step3: Write the equation of the circle

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h=-2\), \(k = -2\), and \(r = 1\) into the formula, we get \((x+2)^2+(y + 2)^2=1\)

Answer:

\((x + 2)^2+(y+2)^2=1\)