Find radius and center of each sphere. x 2 + y 2 + z 2 + 2 x − 2 z = − 1

Question

Find radius and center of each sphere.      x    2    +      y    2    +      z    2    +  2  x  −  2  z  =  −  1

Trevon Hughes · Accepted Answer

x          2        +      y          2        +      z          2        +  2  x  −  2  =  −  1, now groups together and then completed square  (      x          2        +  2  x  )  +      y          2        +  (      z          2        −  2  z  )  =  −  1, each one you comleted   (  b      /    2      )    2   add both side same value  (      x          2        +  2  x  +  1  )  +      y          2        +  (      z          2        −  2  z  +  1  )  =  −  1  +  1  +  1  (  x  +  1      )          2        +      y          2        +  (  z  −  1      )          2        =  1center: (-1,0,1),r=1

alan3885uo · Accepted Answer

x    2    +      y    2    +      z    2    +  2  x  −  2  z  =  −  1      x    2    +  2  x  +      y    2    +      z    2    −  2  z  =  −  1  (      x    2    +  2  x  +  1  )  +      y    2    +  (      z    2    −  2  z  +  1  )  =  −  1  +  1  +  1 You want to complete the square to get the equation into the right form.  (  x  +  1      )    2    +      y    2    +  (  z  −  1      )    2    =  1center: ( -1, 0, 1)radius:       1    =  1

Find radius and center of each sphere. x^2 +y^2 +z^2 +2x-2z=-1

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