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Write the equation of the sphere in standard form. x2 + y2 + z2 + 2x − 4y − 4z = 27. Find its center and radius. center (x, y, z) = radius = radius

          Write the equation of the sphere in standard form. x2 + y2 + z2 + 2x − 4y − 4z = 27. Find its center and radius.
center   (x, y, z) = 
radius =

  

radius
        

Added by Izzy S.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
James Stewart 8th Edition
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Write the equation of the sphere in standard form. x2 + y2 + z2 + 2x − 4y − 4z = 27. Find its center and radius. center (x, y, z) = radius = radius
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Transcript

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00:01 In this problem we have to write the equation of sphere in standard form and find the center and radius.
00:08 So the given equation is x square plus y square plus z square plus 2x minus 4y minus 4z equal to 27.
00:24 So we can write it as x square plus 2x plus 1 and since we have added 1 we have to subtract 1.
00:35 Similarly y square minus 4y plus 4 and since we have added 4 we have to subtract 4 minus 4 plus z square minus 4z plus 4 again we have to subtract minus 4 and this equal to 27.
00:57 So x square plus 2x plus 1 is x plus 1 whole square y square minus 4y plus 4 is y minus 2 whole square and z square minus 4z plus 4 is z minus 2 whole square and minus 1 minus 4 and minus 4 is 9 which equal to 27 plus 9 which is 36 which is equal to 6 square.
01:33 So we get x plus 1 equal to 6 square and the general equation for sphere is x minus a plus y minus b whole square plus z minus c whole square equal to r square...
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