Question 1136326
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<pre>
The diameter length is


{{{sqrt( ((-4)-2)^2  + (3-(-7))^2 + (2-(-2))^2)}}} = {{{sqrt(36 + 100 + 16)}}} = {{{sqrt(152)}}}.


The center is  ({{{(2 + (-4))/2}}}, {{{((-7)+3)/2}}},{{{((-2)+2)/2}}}) = (-1,-2,0).


Therefore, the equation of the sphere is


{{{(x-(-1))^2}}} + {{{(y-(-2))^2}}} + {{{z^2}}} = {{{(sqrt(152)/2)^2}}},   or, equivalently,


{{{(x+1)^2}}} + {{{y+2)^2}}} + {{{z^2}}} = {{{152/4}}},   which is


{{{(x+1)^2}}} + {{{y+2)^2}}} + {{{z^2}}} = 38.    <U>ANSWER</U>

</pre>

Solved.