Question

question determine the equation of the circle graphed below. answer attempt 1 out of 2

Explanation:

Step1: Find the center of the circle

The center of the circle is given by the point \((h, k)\). From the graph, the center is \((-2, -2)\), so \(h = -2\) and \(k = -2\).

Step2: Find the radius of the circle

The radius \(r\) is the distance from the center \((-2, -2)\) to a point on the circle, say \((4, -2)\) (we can also use other points, but this is straightforward). Using the distance formula \(r=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), where \((x_1,y_1)=(-2,-2)\) and \((x_2,y_2)=(4,-2)\).

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Step3: Write the equation of the circle

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\). Substituting \(h = -2\), \(k = -2\), and \(r = 6\) into the formula:

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Answer:

The equation of the circle is \((x + 2)^2+(y + 2)^2 = 36\)