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Math Help - Equation of a Circle HELP!!!

  1. #1
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    Equation of a Circle HELP!!!

    I have not had Math in 4 years! Can somone please show me how to do this problem:

    The equation of a circle is 4x^2+4y^2+32x-32y+92=0
    a. Finde the center (h,k) of the circle (50%)
    b. Find the radius r of the circle (50%)

    a: (h,k) =

    b: r=

    Thank You So Much!
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  2. #2
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    the goal is to get the equation in the following form ...

    (x-h)^2 + (y-k)^2 = r^2

    where (h,k) are the center coordinates and r is the radius.


    4x^2 + 4y^2 + 32x - 32y + 92 = 0

    start by dividing every term by 4 ...

    x^2 + y^2 + 8x - 8y + 23 = 0

    group the x-vales and y-values together, move the constant ...

    x^2 + 8x + y^2 - 8x = -23

    you now want to complete the square for both x and y ... half the coefficient of each linear term, square the result, and add to both sides of the equation ...

    x^2 + 8x + 16 + y^2 - 8x + 16 = -23 + 16 + 16

    factor the quadratic trinomials of x and y ...

    (x + 4)^2 + (y - 4)^2 = 3^2

    now, do you "see" h, k, and r?
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  3. #3
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    Would the correct answer be:

    (h,k) = (-4,4)
    r = 3
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  4. #4
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    yes
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