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12 April, 16:39

What is the center or a circle represented by the equation (x+9) 2 + (y-6) 2 = 10 to the power of 2

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  1. 12 April, 16:50
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    (-9,6)

    Step-by-step explanation:

    The general equation of a circle is given as:

    x²+y²+2gx+2fy+c = 0

    The centre of the circle is (-g,-f)

    Given the equation of the circle

    (x+9) ² + (y-6) ² = 10²

    First we need to expand and write it in the general form. On expansion:

    x²+18x+81+y²-12y+36 = 100

    Collecting like terms

    x²+y²+18x-12y+81+36-100 = 0

    x²+y²+18x-12y+17 = 0

    Comparing to the general equation

    2gx = 18x

    g = 9

    2fy = - 12

    f = - 6

    The center of the circle = (-g, - f)

    = (-9, - (-6))

    = (-9, 6)
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