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Thread: 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: .$\displaystyle
    x^2 + 4x + 5 \:= \:12y - y^2$

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

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

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


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

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