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1 April, 17:08

Write the equation of the sphere in standard form. x^2 + y^2 + z^2 + 2x - 2y - 2z = 22

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  1. 1 April, 19:41
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    Given:

    x^2 + y^2 + z^2 + 2x - 2y - 2z = 22

    group the variables

    x^2+2x + y^2-2y + z^2-2z = 22

    then complete the squares

    x^2+2x+1 + y^2-2y+1 + z^2-2z+1 = 22 + 1 + 1 + 1

    factor and simplify

    (x+1) ^2 + (y-1) ^2 + (z-1) ^2 = 5^2

    Interpretation:

    The centre of the sphere is at (-1,1,1) with a radius of 5
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