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Math Help - Help with Circles please

  1. #1
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    Help with Circles please

    The question states:
    Maraiah is making a graphic design on a computer using a coordinate grid. She began with a circle that has a center (0,0). Then, she drew a congruent cirlce with the equation x^2+y^2+12x+4y+5=0.

    A)what is the radius?

    B)what translation did Maraiah make to draw the second circle?

    What i did was, since the second equation is congruent to the fist one, i replaced the x and y with 0. However, the final statement results to be false. 5=0. And using (x-h)^2+(y-k)^2=r^2, i figured the radius to be 0.... i have no clue on how to this problem. Please guide me! Thanks guys.
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  2. #2
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    Hello, jjkins!

    Maraiah is making a graphic design on a computer using a coordinate grid.
    She began with a circle that has a center (0,0).
    Then, she drew a congruent cirlce with the equation x^2+y^2+12x+4y+5\:=\:0

    A) What is the radius?
    Complete the square . . .


    We have: . (x^2 + 12x \qquad) + (y^2 + 4y \qquad) \;=\;-5

    . . . . . . . . (x^2 + 12x + {\color{blue}36}) + (y^2 + 4y + {\color{red}4}) \;=\;-5 + {\color{blue}36} + {\color{red}4}

    . . . . . . . . . . . (x+6)^2\quad+\quad(y+2)^2\quad \;= \quad\;35


    Radius of both circles: . \sqrt{35}





    B) What translation did Maraiah make to draw the second circle?
    The center of the second circle is: . (\text{-}6,\,\text{-}2)

    She moved the original circle: 6 units to the left and 2 units down.

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