Find an equation for each sphere that passes through the point(5,1,4) and is tangent to all three coordinate planes.

Question

kunstboom8w · Accepted Answer

the general sphere equation is  (  x  −      x          0            )          2        +  (  y  −      y          0            )          2        +  (  z  −      z          0            )          2        =      R          2      ...(1)  (      x          0        ,      y          0        ,      z          0        ) is the centerof spheresince the sphere tangent to all three coordinate planes, we have:      x          0        =      y          0        =      z          0        =  R(1) change to:  (  x  −  R      )          2        +  (  y  −  R      )          2        +  (  z  −  R      )          2        =  Rsphere passes through the point (5,1,4) , we have:  (  5  −  R      )          2        +  (  1  −  R      )          2        +  (  4  −  R      )          2        =  R  ⇒  25  −  10  R  +      R          2        +  1  −  2  R  +      R          2        +  16  −  8  R  +      R          2        =      R          2        2      R          2        −  20  R  +  32  =  0      R          2        −  10  R  +  16  =  0(R-2)(R-8) = 0R=2, or R=8the sphere equations are  (  x  −  2      )          2        +  (  y  −  2      )          2        +  (  z  −  2      )          2        =      2          2      or  (  x  −  8      )          2        +  (  y  −  8      )          2        +  (  z  −  8      )          2        =      8          2

popljuvao69 · Accepted Answer

everything answered above is totally perfect except that 25+1+16=42, and not 25+1+16=32. So, radius equals 3 and 7.

Find an equation for each sphere that passes through the point(5,1,4) and is tangent to all three coordinate planes.

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