The equation of a circle is given in general form. Complete parts a through $$ d $$ to follow the step by step process to sketch the graph of the circle. $$ x^{2}+y^{2}+4 x-8 y+4=0 $$ a) Write the equation of the circle in standard form. The equation is $$ (x+2)^{2}+(y-4)^{2}=16 $$. (Simplify your answer.) b) Determine the center and radius of the circle. The center is $$ (-2,4) $$. (Type an ordered pair.) The radius is $$ \square $$. (Simplify your answer. Type an exact answer, using radicals as needed.)

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The radius is $$4$$. To complete part b, we need to determine the radius of the circle from the standard form of the equation. 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. From the standard form you provided: $$ (x + 2)^2 + (y - 4)^2 = 16 $$ we can see that: - The center $$(h, k)$$ is $$(-2, 4)$$. - The right side of the equation, $$16$$, represents $$r^2$$. To find the radius $$r$$, we take the square root of $$16$$: $$ r = \sqrt{16} = 4 $$ So, the radius is $$4$$. Thus, the completed part b is: The radius is $$4$$.

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