Problem

Find the center and radius of the circle. Write the standard form of the equation. The center of the circle is $(\mathrm{h}, \mathrm{k})=(-3,-1)$ (Type an ordered pair.) The radius of the circle is $r=3$. The equation of the circle in standard form is (Type your answer in standard form.)

Solution

Step 1 :The center of the circle is given as (-3,-1).

Step 2 :The radius of the circle is given as 3.

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

Step 4 :Substitute the given values into the standard form to get the equation of the circle: \((x - (-3))^2 + (y - (-1))^2 = 3^2\).

Step 5 :Simplify the equation to get the final answer: \((x + 3)^2 + (y + 1)^2 = 9\).

Step 6 :Final Answer: The equation of the circle in standard form is \(\boxed{(x + 3)^2 + (y + 1)^2 = 9}\).

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Source: https://solvelyapp.com/problems/7SjMlk7xtW/

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