Question

write the equation of the circle graphed below.

Explanation:

Step1: Find the center of the circle

The center of the circle is at \((-3,-5)\).

Step2: Find the radius of the circle

Count the distance from the center \((-3,-5)\) to a point on the circle (e.g., the blue - marked point \((-7,-2)\)).
Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), let \((x_1,y_1)=(-3,-5)\) and \((x_2,y_2)=(-7,-2)\)

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Step3: Write the equation of the circle

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.
Substitute \(h=-3\), \(k = - 5\), and \(r = 5\) into the formula:

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Answer:

\((x + 3)^2+(y+5)^2=25\)