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29 May, 03:37

What is the center of the equation X^2+y^2-4x-8y-16=0

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  1. 29 May, 03:47
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    x² + y² - 4x - 8y - 16 = 0

    + 16 + 16

    x² + y² - 4x - 8y = 16

    x² - 4x + y² - 8y = 16

    (x² - 4x + 4) + (y² - 8y + 16) = 16 + 4 + 16

    (x² - 2x - 2x + 4) + (y² - 4y - 4y + 16) = 20 + 16

    [x (x) - x (2) - 2 (x) - 2 (-2) ] + [y (y) - y (4) - 4 (y) - 4 (4) ] = 36

    [x (x - 2) - 2 (x - 2) ] + [y (y - 4) - 4 (y - 4) ] = 36

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

    (x - 2) ² + (y - 4) ² = 36

    36 36 36

    ¹/₃₆ (x - 2) ² + ¹/₃₆ (y - 4) ² = 1

    Center: (2, 4)
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