Question

answer attempt 1 out of 2 $(x - 1)^{2}+(y - k)^{2}=$ submit answer

Explanation:

Step1: Find the center of the circle

The center of the circle is \((h,k)=(-6,2)\)

Step2: Use the distance formula to find the radius

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Let \((x_1,y_1)=(-6,2)\) and \((x_2,y_2)=(-4,5)\)

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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 \(h=-6\), \(k = 2\) and \(r=\sqrt{13}\)

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Answer:

\((x + 6)^2+(y - 2)^2=13\)