Write the equation of the circle in the form $(x - h)^{2} + (y - k)^{2} = r^{2}$ $x^{2} + y^{2} + 6 x + 2 y + 3 = 0$ .
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Final Answer: The equation of the circle in the form $(x - h)^{2} + (y - k)^{2} = r^{2}$ is $7$ .

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Step 1 ：The general form of the equation of a circle is $x^{2} + y^{2} + 2 g x + 2 f y + c = 0$ . Comparing this with the given equation, we can see that $g = 3$ , $f = 1$ and $c = 3$ .

Step 2 ：The center of the circle is given by $(- g, - f)$ and the radius is given by $\sqrt{g^{2} + f^{2} - c}$ .

Step 3 ：We can substitute these values into the equations to find the center and radius of the circle.

Step 4 ：Substituting the values we get $h = - 3$ , $k = - 1$ , and $r = 2.6457513110645907$ .

Step 5 ：The equation of the circle in the form $(x - h)^{2} + (y - k)^{2} = r^{2}$ is $(x + 3)^{2} + (y + 1)^{2} = 7$ .

Step 6 ：Final Answer: The equation of the circle in the form $(x - h)^{2} + (y - k)^{2} = r^{2}$ is $7$ .

Write the equation of the circle in the form (x−h)2+(y−k)2=r2 x2+y2+6x+2y+3=0.Submit Question

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Write the equation of the circle in the form $(x - h)^{2} + (y - k)^{2} = r^{2}$ $x^{2} + y^{2} + 6 x + 2 y + 3 = 0$ .
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