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Math Help - Center of a circle

  1. #1
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    Center of a circle

    Please show all steps. Thanks!

    Find the center of the circle that has the equation
    x^2 + 4x + 5 = 12y - y^2
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  2. #2
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    Hello, cam_ddrt!

    You've never done one of these before?
    And no one has ever shown you how?


    Find the center of the circle: . <br />
x^2 + 4x + 5 \:= \:12y - y^2

    Rearrange the terms: . x^2 + 4x + y^2 - 12y \:=\:-5

    Complete the square: . x^2 + 4x + {\color{blue}4} + y^2 - 12y + {\color{red}36} \:=\:-5 + {\color{blue}4} + {\color{red}36}

    And we have: . (x+2)^2 + (y-6)^2 \:=\:35


    The center is: . (-2,\:6)

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