How can I write the equation of a sphere that is centered at the triple point ( 2 , 4 , − 4 ) and passes through the origin.

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How can I write the equation of a sphere that is centered at the triple point   (  2  ,  4  ,  −  4  ) and passes through the origin.

Layla Love · Accepted Answer

Step 1Since the sphere is centered at   (  2  ,  4  ,  −  4  ) and passes through the origin, the distance from the origin to this point must be the radius a of the sphere:  a  =      (    2    −    0          )      2        +    (    4    −    0          )      2        +    (    −    4    −    0          )      2        =  6.Then the equation of the sphere is simply:  (  x  −  2      )    2    +  (  y  −  4      )    2    +  (  z  +  4      )    2    =      a    2    =  36.For the second question, the midpoint is indeed the center of the sphere:   (  3  ,  2  ,  2  ) . The radius is the length from the center to one of the points:   a  =      (    6    −    3          )      2        +    (    0    −    2          )      2        +    (    2    −    2          )      2        =      13   .Then your equations is straightforward:  (  x  −  3      )    2    +  (  y  −  2      )    2    +  (  z  −  2      )    2    =  13. .

tr2os8x · Accepted Answer

Step 1You say that for the right value of a, the equation of the sphere is  (  x  −  2      )    2    +  (  y  −  4      )    2    +  (  z  +  4      )    2    =  a  . .You also say that   (  0  ,  0  ,  0  ) is a point on the sphere. This means that   x  =  0 ,   y  =  0 ,   z  =  0 must satisfy the equation, that is  (  0  −  2      )    2    +  (  0  −  4      )    2    +  (  0  +  4      )    2    =  a  . .

How can I write the equation of a sphere that

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