Find an equation of the sphere that passes through the origin and whose center is (5, -8, -10). the equation equals 0

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Julianna Bell · Accepted Answer

Equation to the sphere with centre   (      x          1        ,      y          1        ,      z          1        ) and radius ais   (  x  −      x          1            )          2        +  (  y  −      y          1            )          2        +  (  z  −      z          1            )          2        =      a          2      here   (      x          1        ,      y          1        ,      z          1        )  =  (  5  ,  −  8  ,  −  10  )i.e.   (  x  −  5      )          2        +  (  y  +  8      )          2        +  (  z  +  10      )          2        =      a          2      and this sphere is passes through the origin so  (  0  −  5      )          2        +  (  0  +  8      )          2        +  (  0  +  10      )          2        =      a          2        ⇒      a          2        =  189Now required sphere equation is  (  x  −  5      )          2        +  (  y  +  8      )          2        +  (  z  +  10      )          2        =  189  ⇒      x          2        +      y          2        +      z          2        +  189  −  189  −  10  x  +  16  y  +  20  z  =  0  ⇒      x          2        +      y          2        +      z          2        −  10  x  +  16  y  +  20  z  =  0

pliwraih · Accepted Answer

the equation of sphere that passes through the origin can be written as      x          2        +      y          2        +      z          2        =      R          2         (R is the radius)since it pass  (5, -8, -10)., we have:      5          2        +  (  −  8      )          2        +  (  −  10      )          2        =      R          2        ⇒      R          2        =  189the equation of sphere is      x          2        +      y          2        +      z          2        =  189  R  =      189   is the radius

Find an equation of the sphere that passes through the origin and whose center is (5, -8, -10). the equation equals 0

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