Find an equation of the circle having the given center and radius. Center $$ (-5,1) $$, radius $$ 2 \sqrt{7} $$ Choose the correct equation. A. $$ (x+5)^{2}+(y-1)^{2}=14 $$ B. $$ (x-5)^{2}+(y+1)^{2}=14 $$ C. $$ (x-5)^{2}+(y+1)^{2}=28 $$ D. $$ (x+5)^{2}+(y-1)^{2}=28 $$

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The correct equation is D. $$ (x+5)^{2}+(y-1)^{2}=28 $$. The standard equation of a circle with center $$(h, k)$$ and radius $$r$$ is given by: $$ (x - h)^2 + (y - k)^2 = r^2 $$ In this case, the center is $$(-5, 1)$$ and the radius is $$2\sqrt{7}$$. First, we need to find $$r^2$$: $$ r^2 = (2\sqrt{7})^2 = 4 \cdot 7 = 28 $$ Now, substituting the center $$(-5, 1)$$ into the standard equation: $$ (x - (-5))^2 + (y - 1)^2 = 28 $$ This simplifies to: $$ (x + 5)^2 + (y - 1)^2 = 28 $$ Now, let's compare this with the options provided: A. $$ (x+5)^{2}+(y-1)^{2}=14 $$ B. $$ (x-5)^{2}+(y+1)^{2}=14 $$ C. $$ (x-5)^{2}+(y+1)^{2}=28 $$ D. $$ (x+5)^{2}+(y-1)^{2}=28 $$ The correct equation is: **D. $$ (x+5)^{2}+(y-1)^{2}=28 $$**.

Find an equation of the circle having the given center and radius. Center \( (-5,1) \), radius \( 2 \sqrt{7} \) Choose the correct equation. A. \( (x+5)^{2}+(y-1)^{2}=14 \) B. \( (x-5)^{2}+(y+1)^{2}=14 \) C. \( (x-5)^{2}+(y+1)^{2}=28 \) D. \( (x+5)^{2}+(y-1)^{2}=28 \)

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Find an equation of the circle having the given center and radius. Center \( (-5,1) \), radius \( 2 \sqrt{7} \) Choose the correct equation. A. \( (x+5)^{2}+(y-1)^{2}=14 \) B. \( (x-5)^{2}+(y+1)^{2}=14 \) C. \( (x-5)^{2}+(y+1)^{2}=28 \) D. \( (x+5)^{2}+(y-1)^{2}=28 \)

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