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March 26, 2017

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write the equation of the circle in standard form. find the center, radius, intercepts, and graph the circle. x^2+y^2-6x-8y+25=36

  • Math - ,

    x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36


    Equation of a circle in standard form :

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


    x ^ 2 + y ^ 2 - 6 x - 8 y + 25 = 36

    x ^ 2 - 6 x + y ^ 2 - 8 y + 25 = 36

    ( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36

    The process involves completing the square separately for the x and y variables.


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    ( x - 3 ) ^ 2 = x ^ 2 - 2 * x * 3 + 3 ^ 2

    ( x - 3 ) ^ 2 = x ^ 2 - 6 x + 9 Subtract 9 to both sides

    ( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x + 9 - 9

    ( x - 3 ) ^ 2 - 9 = x ^ 2 - 6 x

    x ^ 2 - 6 x = ( x - 3 ) ^ 2 - 9



    ( y - 4 ) ^ 2 = y ^ 2 - 2 * y * 4 + 4 ^ 2

    ( y - 4 ) ^ 2 = y ^ 2 - 8 y + 16 Subtract 16 to both sides

    ( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y + 16 -16

    ( y - 4 ) ^ 2 - 16 = y ^ 2 - 8 y

    y ^ 2 - 8 y = ( y - 4 ) ^ 2 - 16

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    ( x ^ 2 - 6 x ) + ( y ^ 2 - 8 y ) + 25 = 36

    ( x - 3 ) ^ 2 - 9 + ( y - 4 ) ^ 2 - 16 + 25 = 36

    (x - 3 ) ^ 2 + ( y - 4 ) ^ 2 - 25 + 25 = 36

    ( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 36


    ( x - 3 ) ^ 2 + ( y - 4 ) ^ 2 = 6 ^ 2

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