Question

determine the equation of the circle graphed below.
the number of attempts on this specific problem before you are marked incorrect

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of a circle's equation is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center of the circle. From the graph, the center \((h,k)=(6,4)\).

Step2: Calculate the radius

Use the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\) to find the radius. Here, \((x_1,y_1)=(6,4)\) (center) and \((x_2,y_2)=(9,5)\) (a point on the circle).

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Step3: Substitute \(h,k,r\) into the standard equation

Substitute \(h = 6\), \(k = 4\), and \(r=\sqrt{10}\) into \((x - h)^2+(y - k)^2=r^2\).

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Answer:

\((x - 6)^2+(y - 4)^2=10\)